UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM N-CSR

CERTIFIED SHAREHOLDER REPORT OF REGISTERED

MANAGEMENT INVESTMENT COMPANIES

Investment Company Act file number: 811-05987

Morgan Stanley New York Municipal Money Market Trust

(Exact name of registrant as specified in charter)

522 Fifth Avenue, New York, New York 10036

(Address of principal executive offices) (Zip code)

Kevin Klingert

522 Fifth Avenue, New York, New York 10036

(Name and address of agent for service)

Registrant’s telephone number, including area code: 212-296-0289

Date of fiscal year end: December 31, 2013

Date of reporting period: June 30, 2013

Item 1 - Report to Shareholders

Trustees

Frank L. Bowman

Michael Bozic

Kathleen A. Dennis

James F. Higgins

Dr. Manuel H. Johnson

Joseph J. Kearns

Michael F. Klein

Michael E. Nugent

W. Allen Reed

Fergus Reid

Officers

Michael E. Nugent

Chairperson of the Board

Kevin Klingert

President and Principal Executive Officer

Mary Ann Picciotto

Chief Compliance Officer

Stefanie V. Chang Yu

Vice President

Francis J. Smith

Treasurer and Principal Financial Officer

Mary E. Mullin

Secretary

Transfer Agent

Boston Financial Data Services, Inc.

2000 Crown Colony Drive

Quincy, Massachusetts 02169

Custodian

State Street Bank and Trust Company

One Lincoln Street

Boston, Massachusetts 02111

Independent Registered Public Accounting Firm

Ernst & Young LLP

200 Clarendon Street

Boston, Massachusetts 02116

Legal Counsel

Dechert LLP

1095 Avenue of the Americas

New York, New York 10036

Counsel to the Independent Trustees

Kramer Levin Naftalis & Frankel LLP

1177 Avenue of the Americas

New York, New York 10036

Adviser

Morgan Stanley Investment Management Inc.

522 Fifth Avenue

New York, New York 10036

The financial statements included herein have been taken from the records of the Fund without examination by the independent auditors and accordingly they do not express an opinion thereon.

This report is submitted for the general information of the shareholders of the Fund. For more detailed information about the Fund, its fees and expenses and other pertinent information, please read its Prospectus. The Fund’s Statement of Additional Information contains additional information about the Fund, including its trustees. It is available, without charge, by calling (800) 869-NEWS.

This report is not authorized for distribution to prospective investors in the Fund unless preceded or accompanied by an effective Prospectus. Please read the Prospectus carefully before investing.

Morgan Stanley Distribution, Inc., member FINRA.

© 2013 Morgan Stanley

DWNSAN

705311 EXP [08/31/14]

INVESTMENT MANAGEMENT

Morgan Stanley

New York Municipal

Money Market Trust

Semiannual

Report

June 30, 2013

Morgan Stanley New York Municipal Money Market Trust

Table of Contents

Welcome Shareholder	3
Fund Report	4
Expense Example	7
Investment Advisory Agreement Approval	8
Portfolio of Investments	11
Statement of Assets and Liabilities	15
Statement of Operations	16
Statements of Changes in Net Assets	17
Notes to Financial Statements	18
Financial Highlights	24
U.S. Privacy Policy	26

2

Welcome Shareholder,

We are pleased to provide this semiannual report, in which you will learn how your investment in Morgan Stanley New York Municipal Money Market Trust performed during the latest six-month period. It includes an overview of the market conditions and discusses some of the factors that affected performance during the reporting period. In addition, the report contains financial statements and a list of portfolio holdings.

Morgan Stanley Investment Management is a client-centric, investor-led organization. Our global presence, intellectual capital, and breadth of products and services enable us to partner with investors to meet the evolving challenges of today’s financial markets. We aim to deliver superior investment service and to empower our clients to make the informed decisions that help them reach their investment goals.

As always, we thank you for selecting Morgan Stanley Investment Management, and look forward to working with you in the months and years ahead.

This material must be preceded or accompanied by a prospectus for the fund being offered.

Market forecasts provided in this report may not necessarily come to pass. There is no assurance that a mutual fund will achieve its investment objective. An investment in a money market fund is not insured or guaranteed by the Federal Deposit Insurance Corporation or any other government agency. Although the Fund seeks to preserve the value of an investment at $1.00 per share, it is possible to lose money by investing in the Fund. Please see the prospectus for more complete information on investment risks.

3

Fund Report (unaudited)

For the six months ended June 30, 2013

Market Conditions

Rates in the tax-exempt market continued to move down on the shorter end of the curve. The Securities Industry and Financial Markets Association (SIFMA) Index of weekly variable rate securities, at 0.06 percent as of the end of June, matched the prior historical low set in January 2012. The Municipal Market Data (MMD) One-Year Note Index fell two basis points last month to 0.18 percent, its first change since early January.

Broadly speaking, municipal fundamentals continued to improve as most states and many local governments have recovered slowly from the recession. State and local tax collections rose in the first half of the year as an expanding economy and tax increases passed during the recession eased city and state budget woes. While state tax revenue has improved considerably over the past year, local governments continue to struggle in large part because of falling property values. State governments collect most of their revenue from sales and income taxes, which fell fast in response to recessions but also snap back quickly.

In particular, state general funds have shown consecutive quarters of growth in personal income tax and sales tax revenue, both important sources of revenue. In 32 states for which data are available, state tax collections in the first ten months of fiscal year 2013 were 5.7 percent higher than in the same period last year, on average. Revenue is exceeding forecasts in 30 states this budget year, ending this month in most states, according to a report released on June 13 by the National Governors Association. That is helping lift spending to a record $699.2 billion, surpassing the previous high in 2008 as the recession took hold.

That said, the unemployment rate remains high and the economic recovery is relatively weak compared to other post-recessionary periods. State operating budgets could be constrained by elevated expenditure pressures and slow revenue growth in the upcoming fiscal year. States are challenged with providing resources for critical areas that were cut back in the recession, declining federal funds for state programs subject to sequestration, and continued spending demands in areas directly impacted by the sluggish economy, such as Medicaid, higher education and corrections. In response to these challenges and other factors, governors’ recommended budgets indicate that most states will moderately increase spending in fiscal 2014.

June 30 marked the end of most state and local governments’ fiscal years. Almost all state and local governments are required by their constitutions or charters to pass balanced budgets. While it may be difficult politically, simply practicing fiscal austerity should be enough for states to overcome near term fiscal challenges. Budgets will likely be passed and state finances could improve as the economy continues to recover.

In March, New York State adopted a new budget for fiscal 2014, the third year in a row that the state has adopted a budget before the fiscal year’s start on April 1. This is the first time since 1984 that the state has made the deadline for three years in a row. The budget closed a $1.3 billion gap without new taxes or fees. State government approved a total operating budget of $90.2 billion and a $135.1 billion all funds budget (excluding Hurricane Sandy and the Affordable Care Act expenses).

4

At the end of June, Governor Andrew Cuomo and state legislators announced an agreement on legislation to create a Financial Restructuring Board for local governments. The board would provide plans to local governments struggling with financial problems. Local governments that request and accept the board’s plan would be contractually obligated to follow it. The board also offers a binding arbitration process for municipalities and public sector unions if both parties agree to use it.

Performance Analysis

As of June 30, 2013, Morgan Stanley New York Municipal Money Market Trust had net assets of approximately $1.3 billion and an average portfolio maturity of 24 days. For the six-month period ended June 30, 2013, the Fund’s Class R and Class S shares provided a total return of 0.00 percent. For the seven-day period ended June 30, 2013, the Fund’s Class R and Class S shares provided an effective annualized yield of 0.01 percent (subsidized) and -0.46 percent (non-subsidized) and a current yield of 0.01 percent (subsidized) and -0.46 percent (non-subsidized), while its 30-day moving average yield for June was 0.01 percent (subsidized) and -0.45 percent (non-subsidized). Yield quotations more closely reflect the current earnings of the Fund. The non-subsidized yield reflects what the yield would have been had a fee and/or expense waiver not been in place during the period shown. Past performance is no guarantee of future results.

In the on-going environment of extremely low interest rates and struggling economies around the globe, our strategy remains focused on diligent oversight of credit quality, portfolio maturity and diversification. Maintaining high levels of liquidity and protecting principal are the highest priorities. As of the end of the period, the portfolio’s weighted average maturity (WAM) and weighted average life (WAL) were each 24 days.

With the performance of the economy still lackluster and longed-for optimism struggling to surface, we remain committed to a cautious approach. We believe interest rates are likely to stay at exceptionally low levels until the Federal Reserve sees clear signs that the targets for unemployment and inflation are being met. In this uncertain atmosphere, we will carefully monitor state and local economic and budgetary developments.

There is no guarantee that any sectors mentioned will continue to perform as discussed herein or that securities in such sectors will be held by the Fund in the future.

PORTFOLIO COMPOSITION as of 06/30/13
Weekly Variable Rate Bonds	73.2	%
Daily Variable Rate Bonds	9.9
Municipal Bonds & Notes	6.6
Commercial Paper	5.3
Closed-End Investment Companies	2.8
Put Option Bond	2.2

MATURITY SCHEDULE as of 06/30/13
1 – 30 Days	89.1	%
31 – 60 Days	6.2
121 + Days	4.7

Subject to change daily. Provided for informational purposes only and should not be deemed as a recommendation to buy or sell the securities mentioned above. Portfolio composition and maturity schedule are as a percentage of total investments.

Morgan Stanley is a full-service securities firm engaged in securities trading and brokerage activities, investment banking, research and analysis, financing and financial advisory services.

5

Investment Strategy

The Fund will invest in high quality, short-term securities that are normally municipal obligations that pay interest exempt from federal and New York income taxes. The “Adviser” Morgan Stanley Investment Management Inc., seeks to maintain the Fund’s share price at $1.00. The share price remaining stable at $1.00 means that the Fund would preserve the principal value of your investment.

An investment in the Fund is not insured or guaranteed by the Federal Deposit Insurance Corporation or any other government agency. Although the Fund seeks to preserve the value of your investment at $1.00 per share, it is possible to lose money by investing in the Fund.

For More Information

About Portfolio Holdings

Each Morgan Stanley fund provides a complete schedule of portfolio holdings in its semiannual and annual reports within 60 days of the end of the fund’s second and fourth fiscal quarters. The semiannual reports and the annual reports are filed electronically with the Securities and Exchange Commission (SEC) on Form N-CSRS and Form N-CSR, respectively. Morgan Stanley also delivers the semiannual and annual reports to fund shareholders and makes these reports available on its public web site, www.morganstanley.com. Each Morgan Stanley fund also files a complete schedule of portfolio holdings with the SEC for the fund’s first and third fiscal quarters on Form N-Q and monthly holdings for each money market fund on Form N-MFP. Morgan Stanley does not deliver these reports to shareholders, nor are the first and third fiscal quarter reports posted to the Morgan Stanley public web site. However, the holdings for each money market fund are posted to the Morgan Stanley public web site. You may obtain the Form N-Q filings (as well as the Form N-CSR, N-CSRS and N-MFP filings) by accessing the SEC’s web site, http://www.sec.gov. You may also review and copy them at the SEC’s public reference room in Washington, DC. Information on the operation of the SEC’s public reference room may be obtained by calling the SEC at (800) SEC-0330. You can also request copies of these materials, upon payment of a duplicating fee, by electronic request at the SEC’s e-mail address (publicinfo@sec.gov) or by writing the public reference section of the SEC, Washington, DC 20549-1520.

Householding Notice

To reduce printing and mailing costs, the Fund attempts to eliminate duplicate mailings to the same address. The Fund delivers a single copy of certain shareholder documents, including shareholder reports, prospectuses and proxy materials, to investors with the same last name who reside at the same address. Your participation in this program will continue for an unlimited period of time unless you instruct us otherwise. You can request multiple copies of these documents by calling (800) 869-NEWS, 8:00 a.m. to 8:00 p.m., ET. Once our Customer Service Center has received your instructions, we will begin sending individual copies for each account within 30 days.

6

Expense Example (unaudited)

As a shareholder of the Fund, you incur ongoing costs, including advisory fees; administration fees; shareholder services fees; and other Fund expenses. This example is intended to help you understand your ongoing costs (in dollars) of investing in the Fund and to compare these costs with the ongoing costs of investing in other mutual funds.

This example is based on an investment of $1,000 invested at the beginning of the period and held for the entire period 01/01/13 – 06/30/13.

Actual Expenses

The first line of the table below provides information about actual account values and actual expenses. You may use the information in this line, together with the amount you invested, to estimate the expenses that you paid over the period. Simply divide your account value by $1,000 (for example, an $8,600 account value divided by $1,000 = 8.6), then multiply the result by the number in the first line under the heading entitled “Expenses Paid During Period” to estimate the expenses you paid on your account during this period.

Hypothetical Example for Comparison Purposes

The second line of the table below provides information about hypothetical expenses based on the Fund’s actual expense ratio and an assumed rate of return of 5% per year before expenses, which is not the Fund’s actual return. The hypothetical account values and expenses may not be used to estimate the actual ending account balance or expenses you paid for the period. You may use this information to compare the ongoing cost of investing in the Fund and other funds. To do so, compare this 5% hypothetical example with the 5% hypothetical examples that appear in the shareholder reports of the other funds.

Please note that the expenses shown in the table are meant to highlight your ongoing costs only. Therefore, the second line of the table is useful in comparing ongoing costs, and will not help you determine the relative total cost of owning different funds that have transactional costs, such as sales charges (loads) or exchange fees.

	Beginning Account Value		Ending Account Value		Expenses Paid During Period@
	01/01/13		06/30/13		01/01/13 – 06/30/13
Class R
Actual (0.00% return)	$	1,000.00	$	1,000.05	$	0.59
Hypothetical (5% annual return before expenses)	$	1,000.00	$	1,023.93	$	0.60
Class S
Actual (0.00% return)	$	1,000.00	$	1,000.05	$	0.59
Hypothetical (5% annual return before expenses)	$	1,000.00	$	1,023.93	$	0.60

@ Expenses are equal to the Fund’s annualized expense ratios of 0.12% and 0.12% for Class R and Class S shares, respectively, multiplied by the average account value over the period, multiplied by 179^@@/365 (to reflect the one-half year period). If the Fund had borne all of its expenses, the annualized expense ratios would have been 0.55% and 0.55% for Class R and Class S shares, respectively.

@@ Adjusted to reflect non-business day accruals.

7

Investment Advisory Agreement Approval (unaudited)

Nature, Extent and Quality of Services

The Board reviewed and considered the nature and extent of the investment advisory services provided by the Investment Adviser (as defined herein) under the advisory agreement, including portfolio management, investment research and equity and fixed income securities trading. The Board also reviewed and considered the nature and extent of the non-advisory, administrative services provided by the Fund’s Administrator (as defined herein) under the administration agreement, including accounting, clerical, bookkeeping, compliance, business management and planning, and the provision of supplies, office space and utilities at the Investment Adviser’s expense. (The Investment Adviser and the Administrator together are referred to as the “Adviser” and the advisory and administration agreements together are referred to as the “Management Agreement.”) The Board also compared the nature of the services provided by the Adviser with similar services provided by non-affiliated advisers as reported to the Board by Lipper, Inc. (“Lipper”).

The Board reviewed and considered the qualifications of the portfolio managers, the senior administrative managers and other key personnel of the Adviser who provide the administrative and advisory services to the Fund. The Board determined that the Adviser’s portfolio managers and key personnel are well qualified by education and/or training and experience to perform the services in an efficient and professional manner. The Board concluded that the nature and extent of the advisory and administrative services provided were necessary and appropriate for the conduct of the business and investment activities of the Fund and supported its decision to approve the Management Agreement.

Performance, Fees and Expenses of the Fund

The Board reviewed the performance, fees and expenses of the Fund compared to its peers, as determined by Lipper, and to appropriate benchmarks where applicable. The Board discussed with the Adviser the performance goals and the actual results achieved in managing the Fund. When considering a fund’s performance, the Board and the Adviser place emphasis on trends and longer-term returns (focusing on one-year, three-year and five-year performance as of December 31, 2012, or since inception, as applicable). When a fund underperforms its benchmark and/or its peer group average, they discuss the causes of such underperformance and, where necessary, they discuss specific changes to investment strategy or investment personnel. The Board noted that the Fund’s performance was below its peer group average for the three- and five-year periods and equal to its peer group average for the one-year period. The Board discussed with the Adviser the level of the advisory and administration fees (together, the “management fee”) for this Fund relative to comparable funds and/or other accounts advised by the Adviser and/or compared to its peers as determined by Lipper. In addition to the management fee, the Board also reviewed the Fund’s total expense ratio. The Board noted that both the Fund’s management fee and total expense ratio were lower than its peer

8

group averages. After discussion, the Board concluded that the Fund’s (i) performance was acceptable, and (ii) management fee and total expense ratio were competitive with its peer group averages.

Economies of Scale

The Board considered the size and growth prospects of the Fund and how that relates to the Fund’s total expense ratio and particularly the Fund’s management fee rate, which includes breakpoints. In conjunction with its review of the Adviser’s profitability, the Board discussed with the Adviser how a change in assets can affect the efficiency or effectiveness of managing the Fund and whether the management fee level is appropriate relative to current and projected asset levels and/or whether the management fee structure reflects economies of scale as asset levels change. The Board has determined that its review of the actual and potential economies of scale of the Fund supports its decision to approve the Management Agreement.

Profitability of the Adviser and Affiliates

The Board considered information concerning the costs incurred and profits realized by the Adviser and its affiliates during the last year from their relationship with the Fund and during the last two years from their relationship with the Morgan Stanley Fund Complex and reviewed with the Adviser the cost allocation methodology used to determine the profitability of the Adviser and affiliates. The Board has determined that its review of the analysis of the Adviser’s expenses and profitability supports its decision to approve the Management Agreement.

Other Benefits of the Relationship

The Board considered other benefits to the Adviser and its affiliates derived from their relationship with the Fund and other funds advised by the Adviser. These benefits may include, among other things, “float” benefits derived from handling of checks for purchases and sales, research received by the Adviser generated from commission dollars spent on funds’ portfolio trading and fees for distribution and/or shareholder servicing. The Board reviewed with the Adviser each of these arrangements and the reasonableness of the Adviser’s costs relative to the services performed. The Board has determined that its review of the other benefits received by the Adviser or its affiliates supports its decision to approve the Management Agreement.

Resources of the Adviser and Historical Relationship Between the Fund and the Adviser

The Board considered whether the Adviser is financially sound and has the resources necessary to perform its obligations under the Management Agreement. The Board also reviewed and considered the historical relationship between the Fund and the Adviser, including the organizational structure of the Adviser, the policies and procedures formulated and adopted by the Adviser for managing the Fund’s operations and the

9

Board’s confidence in the competence and integrity of the senior managers and key personnel of the Adviser. The Board concluded that the Adviser has the financial resources necessary to fulfill its obligations under the Management Agreement and that it is beneficial for the Fund to continue its relationship with the Adviser.

Other Factors and Current Trends

The Board considered the controls and procedures adopted and implemented by the Adviser and monitored by the Fund’s Chief Compliance Officer and concluded that the conduct of business by the Adviser indicates a good faith effort on its part to adhere to high ethical standards in the conduct of the Fund’s business.

General Conclusion

After considering and weighing all of the above factors, the Board concluded that it would be in the best interest of the Fund and its shareholders to approve renewal of the Management Agreement for another year. In reaching this conclusion the Board did not give particular weight to any single factor referenced above. The Board considered these factors over the course of numerous meetings, some of which were in executive session with only the independent Board members and their counsel present. It is possible that individual Board members may have weighed these factors differently in reaching their individual decisions to approve the Management Agreement.

10

Morgan Stanley New York Municipal Money Market Trust

Portfolio of InvestmentsⁿJune 30, 2013 (unaudited)

PRINCIPAL AMOUNT (000)			COUPON RATE (a)	DEMAND DATE (b)	MATURITY DATE		VALUE
		Weekly Variable Rate Bonds (73.3%)
$	9,575	Amherst Development Corporation, NY, Student Housing Facility South Lake Village Ser 2010 B	0.11%	07/05/13		10/01/35	$	9,575,000
	9,880	Deutsche Bank SPEARS, NY, New York State Dormitory Authority Personal Income Tax Ser 2011 C SPEARS Ser DB 1072X (c)	0.08	07/05/13		03/15/41		9,880,000
	10,600	Long Island Power Authority, NY, Electric System Ser 2012 C	0.06	07/05/13		05/01/33		10,600,000
		Metropolitan Transportation Authority, NY,
	18,700	Dedicated Tax Ser 2008 B-1	0.05	07/05/13		11/01/34		18,700,000
	31,400	Ser 2002 G Subser G-1	0.05	07/05/13		11/01/26		31,400,000
		New York City Cultural Resources Trust, NY,
	34,690	American Museum of Natural History Ser 2008 B1	0.05	07/05/13		04/01/44		34,690,000
	1,400	Juilliard School Ser 2009 A ROCs II-R Ser 11927 (c)	0.07	07/05/13		01/01/33		1,400,000
	31,400	New York Botanical Garden Ser 2009 A	0.08	07/05/13		07/01/32		31,400,000
	6,700	The Metropolitan Museum of Art Ser 2006 A-1	0.07	07/05/13		10/01/36		6,700,000
		New York City Health & Hospitals Corporation, NY,
	8,800	Health System Ser 2008 B	0.05	07/05/13		02/15/31		8,800,000
	12,370	Health System Ser 2008 C	0.05	07/05/13		02/15/31		12,370,000
	19,900	New York City Housing Development Corporation, NY, 245 East 124th Street Ser 2008 A	0.06	07/05/13		11/01/46		19,900,000
		New York City Industrial Development Agency, NY,
	4,580	Auditory & Oral School Ser 2006	0.06	07/05/13		12/01/32		4,580,000
	9,585	Civic Facilities New York Law School Ser 2006 B-1	0.05	07/05/13		07/01/36		9,585,000
		New York City Transitional Finance Authority, NY,
	2,200	Future Tax Fiscal 2010 Ser F Subser F-5	0.06	07/05/13		02/01/35		2,200,000
	2,400	Future Tax Fiscal 2012 Ser D-1 ROCs II-R Ser 11994 (c)	0.06	07/05/13		11/01/19		2,400,000
	9,200	Future Tax Fiscal 2013 Ser A Subser A-7	0.04	07/05/13		08/01/39		9,200,000
	12,275	Recovery Fiscal 2003 Ser 3 Subser 3G	0.05	07/05/13		11/01/22		12,275,000
		New York City, NY,
	33,800	Fiscal 2003 Subser C-5	0.05	07/05/13		08/01/20		33,800,000
	6,875	Fiscal 2004 Subser A-5	0.06	07/05/13		08/01/31		6,875,000
	10,575	Fiscal 2004 Subser A-6	0.06	07/05/13		08/01/31		10,575,000
	25,800	Fiscal 2006 Subser F-4 A	0.05	07/05/13		09/01/35		25,800,000
	25,500	Fiscal 2006 Subser F-4 B	0.06	07/05/13		09/01/35		25,500,000
	18,735	Fiscal 2008 Subser B-3	0.05	07/05/13		09/01/27		18,735,000
	19,320	Fiscal 2008 Subser J-9	0.05	07/05/13		08/01/27		19,320,000
	14,300	Fiscal 2010 Subser G-4	0.05	07/05/13		03/01/39		14,300,000
	6,200	Fiscal 2013 Ser D & E ROCs II-R Ser 14045 (c)	0.07	07/05/13		08/01/20		6,200,000
		New York State Dormitory Authority,
	9,060	Catholic Health System Ser 2006 A	0.06	07/05/13		07/01/25		9,060,000
	6,770	Catholic Health System Ser 2008	0.06	07/05/13		07/01/34		6,770,000
	10,000	City University System Cons 5th Ser 2008 C	0.06	07/05/13		07/01/31		10,000,000
	13,000	City University System Cons 5th Ser 2008 D	0.05	07/05/13		07/01/31		13,000,000

See Notes to Financial Statements

11

Morgan Stanley New York Municipal Money Market Trust

Portfolio of InvestmentsⁿJune 30, 2013 (unaudited)  continued

PRINCIPAL AMOUNT (000)			COUPON RATE (a)	DEMAND DATE (b)	MATURITY DATE		VALUE
$	5,000	Columbia University Ser 2003 B	0.05%	07/05/13		07/01/28	$	5,000,000
	37,100	Columbia University Ser 2009 A	0.04	07/05/13		09/01/39		37,100,000
	18,320	Cornell University Ser 2000 B	0.07	07/05/13		07/01/30		18,320,000
	4,500	Cornell University Ser 2004 A	0.05	07/05/13		07/01/33		4,500,000
	19,500	Cornell University Ser 2004 B	0.05	07/05/13		07/01/33		19,500,000
	11,090	Mental Health Services Facilities Ser 2003D-2E	0.05	07/05/13		02/15/31		11,090,000
	9,390	Mental Health Services Facilities Ser 2003D-2F	0.05	07/05/13		02/15/31		9,390,000
	28,305	Mental Health Services Facilities Ser 2003D-2H	0.05	07/05/13		02/15/31		28,305,000
	15,660	New York Law School Ser 2009	0.05	07/05/13		07/01/38		15,660,000
	20,000	Personal Income Tax Education Ser 2006 D Eagle #20060164 Class A (c)	0.09	07/05/13		03/15/36		20,000,000
	11,000	Personal Income Tax Education Ser 2006 D ROCs II-R Ser 12106 (c)	0.06	07/05/13		04/01/15		11,000,000
	2,300	Personal Income Tax Ser 2011 A ROCs II-R Ser 11975 (c)	0.06	07/05/13		03/15/19		2,300,000
	11,390	Pratt Institute Ser 2009 A	0.11	07/05/13		07/01/28		11,390,000
	7,570	Pratt Institute Ser 2009 B	0.11	07/05/13		07/01/34		7,570,000
	28,900	Rockefeller University Ser 2008 A	0.06	07/05/13		07/01/39		28,900,000
	28,050	Rockefeller University Ser 2009 B	0.05	07/05/13		07/01/40		28,050,000
	5,400	Rockefeller University Ser 2009-C ROCs II-R Ser 11944 (c)	0.06	07/05/13		07/01/34		5,400,000
	2,613	The Metropolitan Museum of Art Ser A	0.07	07/05/13		07/01/15		2,613,000
	4,790	The Metropolitan Museum of Art Ser B	0.07	07/05/13		07/01/23		4,790,000
	3,495	New York State Environmental Facilities Corporation, Clean Water & Drinking Ser 2008 B PUTTERs Ser 2900 (c)	0.07	07/05/13		12/15/15		3,495,000
		New York State Housing Finance Agency,
	21,290	80 DeKalb Avenue 2009 Ser A	0.05	07/05/13		05/01/42		21,290,000
	21,340	80 DeKalb Avenue 2009 Ser B	0.05	07/05/13		05/01/42		21,340,000
	19,750	Avalon Bowery Place I Ser 2010 A	0.06	07/05/13		11/01/37		19,750,000
	31,025	Related-Taconic West 17th Street Ser 2009 A	0.06	07/05/13		05/15/39		31,025,000
	12,000	Riverside Center 2 Ser 2012 A	0.07	07/05/13		11/01/46		12,000,000
		New York State Local Government Assistance Corporation,
	18,305	Ser 2008 B	0.05	07/05/13		04/01/21		18,305,000
	19,800	Sub Lien Ser 2003 A-8V	0.05	07/05/13		04/01/19		19,800,000
		New York State Mortgage Agency,
	5,000	Homeowner Mortgage Ser 129 (AMT)	0.08	07/05/13		10/01/35		5,000,000
	15,000	Homeowner Mortgage Ser 159	0.06	07/05/13		10/01/38		15,000,000
	2,800	New York State Thruway Authority, Highway & Bridge Trust Fund Ser 2011 A-1 ROCs II-R Ser 11997 (c)	0.07	07/05/13		04/01/19		2,800,000
		New York State Urban Development Corporation,
	7,420	Personal Income Tax Ser B PUTTERs Ser 2887 (c)	0.07	07/05/13		03/15/15		7,420,000
	9,600	Service Contract Ser 2008-A-1	0.05	07/05/13		01/01/30		9,600,000
	15,200	Service Contract Ser 2008-A-5	0.05	07/05/13		01/01/30		15,200,000

See Notes to Financial Statements

12

Morgan Stanley New York Municipal Money Market Trust

Portfolio of InvestmentsⁿJune 30, 2013 (unaudited)  continued

PRINCIPAL AMOUNT (000)			COUPON RATE (a)			DEMAND DATE (b)	MATURITY DATE		VALUE
$	10,000	Rib Floater Credit Enhanced Trust, PR, Puerto Rico Sales Tax Financing Corporation Jr. Lien BANs Ser 2013A Trust Receipts Ser 2013 FR-8WE (c)		0.11%		07/05/13		09/30/14	$	10,000,000
	30,000	Triborough Bridge & Tunnel Authority, NY, Subser 2001 B		0.06		07/05/13		01/01/32		30,000,000
	7,210	Wells Fargo Stage Trust, NY, New York City Municipal Water Finance Authority Ser 2012 FF Stage Trust Ser 54C (c)		0.06		07/05/13		06/15/45		7,210,000
		Total Weekly Variable Rate Bonds (Cost $955,703,000)								955,703,000
		Daily Variable Rate Bonds (9.9%)
	1,350	Nassau County Industrial Development Agency, NY, Cold Spring Harbor Laboratory Ser 1999		0.05		07/01/13		01/01/34		1,350,000
	6,000	New York City Cultural Resources Trust, NY, Lincoln Center Ser 2008 A-1 (c)		0.05		07/01/13		12/01/35		6,000,000
		New York City Municipal Water Finance Authority, NY,
	7,450	Second General Fiscal 2007 Ser CC-1		0.07		07/01/13		06/15/38		7,450,000
	650	Second General Fiscal 2011 Ser FF-1		0.08		07/01/13		06/15/44		650,000
	3,340	Second General Fiscal 2012 Ser A-1		0.04		07/01/13		06/15/44		3,340,000
	9,900	Second General Fiscal 2012 Ser B-4		0.04		07/01/13		06/15/45		9,900,000
	7,950	Water & Sewer System Fiscal 2011 Ser DD-2		0.03		07/01/13		06/15/43		7,950,000
		New York City Transitional Finance Authority, NY,
	18,500	Future Tax Fiscal 2010 Ser G Subser G5		0.05		07/02/13		05/01/34		18,500,000
	12,200	Recovery Fiscal 2003 Ser 3 Subser 3H		0.03		07/01/13		11/01/22		12,200,000
		New York City, NY,
	8,300	Fiscal 2006 Subser I-8		0.07		07/01/13		04/01/36		8,300,000
	14,000	Fiscal 2008 Ser J Subser J-3		0.05		07/02/13		08/01/23		14,000,000
	5,500	Fiscal 2008 Subser L-4		0.04		07/01/13		04/01/38		5,500,000
	7,200	Fiscal 2012 Ser A Subser A-5		0.04		07/01/13		08/01/36		7,200,000
	10,050	Fiscal 2012 Subser G-6		0.04		07/01/13		04/01/42		10,050,000
	11,235	Fiscal 2013 Ser A-2		0.06		07/01/13		10/01/38		11,235,000
	5,300	Fiscal 2013 Ser F Subser F-3		0.08		07/01/13		03/01/42		5,300,000
		Total Daily Variable Rate Bonds (Cost $128,925,000)								128,925,000
			COUPON RATE			YIELD TO MATURITY ON DATE OF PURCHASE
		Municipal Bonds & Notes (6.6%)
	9,070	Auburn City School District, NY, Ser 2013 BANS, dtd 06/25/13		1.00	%	0.30%		06/25/14		9,132,525
	11,978	Columbia County, NY, Ser 2013 BANs, dtd 05/09/13		1.00		0.30		05/09/14		12,050,023
	13,185	Hempstead Union Free School District, NY, Ser 2012 BANs, dtd 07/19/12		1.50		0.29		07/19/13		13,193,713
	2,159	Lewiston Town, NY, Ser 2012 BANs, dtd 08/14/12		1.25		0.45		07/25/13		2,160,386
	7,340	Mount Vernon City School District, NY, Ser 2012 BANs, dtd 08/23/12		1.25		0.45		08/23/13		7,348,804

See Notes to Financial Statements

13

Morgan Stanley New York Municipal Money Market Trust

Portfolio of InvestmentsⁿJune 30, 2013 (unaudited)  continued

PRINCIPAL AMOUNT (000)			COUPON RATE		YIELD TO MATURITY ON DATE OF PURCHASE	MATURITY DATE			VALUE
$	4,000	New York State, Ser 2011 A, dtd 06/19/13		5.00%	0.18%		02/15/14		$	4,121,002
	25,000	New York State Thruway Authority, General Ser 2013 A BANs, dtd 02/07/13		1.00	0.25		07/31/13			25,016,414
	2,257	Ossining Village, NY, Ser 2012 A BANs, dtd 11/20/12		1.00	0.48		11/20/13			2,261,136
	5,000	Schenectady Metroplex Development Authority, NY, Ser 2013 BANs, dtd 01/24/13		1.25	0.43		01/23/14			5,023,257
	3,325	Southeast Town, NY, Ser 2012 BANs, dtd 10/11/12		1.25	0.52		07/11/13			3,325,796
	2,500	Tompkins County, NY, Ser 2012 BANs, dtd 07/27/12		1.25	0.38		07/26/13			2,501,602
		Total Municipal Bonds & Notes (Cost $86,134,658)								86,134,658
		Commercial Paper (5.3%)
		Long Island Power Authority, NY,
	21,192	Electric System Ser 2008 CP-3		0.16	0.16		07/09/13			21,192,000
	21,193	Electric System Ser 2008 CP-3		0.17	0.17		08/07/13			21,193,000
	27,420	Metropolitan Transportation Authority, NY, Ser CP-2 Subser B		0.17	0.17		08/07/13			27,420,000
		Total Commercial Paper (Cost $69,805,000)								69,805,000
			COUPON RATE (a)		DEMAND DATE (b)
		Closed-End Investment Companies (2.8%)
	34,500	Nuveen New York Performance Plus Municipal Fund, Inc., VRDP Ser 1-890 (AMT) (c)		0.17%	07/05/13		03/01/40			34,500,000
	2,000	Nuveen New York Quality Income Municipal Fund, Inc., VRDP Ser 1-1617 (AMT) (c)		0.14	07/05/13		12/01/40			2,000,000
		Total Closed-End Investment Companies (Cost $36,500,000)								36,500,000
		Put Option Bond (2.2%)
	29,000	New York Liberty Development Corporation, 3 World Trade Center Ser 2011 A (Cost $29,000,000)		0.23	06/19/14		12/01/49			29,000,000
		Total Investments (Cost $1,306,067,658)					100.1	%		1,306,067,658
		Liabilities in Excess of Other Assets					(0.1	)		(1,540,192	)
		Net Assets					100.0	%	$	1,304,527,466

AMT	Alternative Minimum Tax.
BANs	Bond Anticipation Notes.
PUTTERS	Puttable Tax-Exempt Receipts.
ROCs	Reset Option Certificates.
VRDP	Variable Rate Demand Preferred.
(a)	Rate shown is the rate in effect at June 30, 2013.
(b)	Date on which the principal amount can be recovered through demand.
(c)	144A security – Certain conditions for public sale may exist. Unless otherwise noted, these securities are deemed to be liquid.

See Notes to Financial Statements

14

Morgan Stanley New York Municipal Money Market Trust

Financial Statements

Statement of Assets and Liabilities

June 30, 2013 (unaudited)

Assets:
Investments in securities, at value (cost $1,306,067,658)	$	1,306,067,658
Cash		80,324
Receivable for:
Shares of beneficial interest sold		9,850,915
Interest		716,302
Prepaid expenses and other assets		50,715
Total Assets		1,316,765,914
Liabilities:
Payable for:
Shares of beneficial interest redeemed		11,975,978
Transfer agent fee		80,284
Administration fee		51,576
Advisory fee		11,674
Accrued expenses and other payables		118,936
Total Liabilities		12,238,448
Net Assets	$	1,304,527,466
Composition of Net Assets:
Paid-in-capital	$	1,304,545,545
Dividends in excess of net investment income		(23,374	)
Accumulated undistributed net realized gain		5,295
Net Assets	$	1,304,527,466
Class R Shares:
Net Assets		$361,674,116
Shares Outstanding (unlimited shares authorized, $0.01 par value)		361,631,178
Net Asset Value Per Share		$1.00
Class S Shares:
Net Assets		$942,853,350
Shares Outstanding (unlimited shares authorized, $0.01 par value)		942,771,932
Net Asset Value Per Share		$1.00

See Notes to Financial Statements

15

Morgan Stanley New York Municipal Money Market Trust

Financial Statements  continued

Statement of Operations

For the six months ended June 30, 2013 (unaudited)

Net Investment Income:
Interest	$	906,813
Dividends from affiliate (Note 5)		234
Total Income		907,047
Expenses
Advisory fee (Note 3)		2,519,742
Shareholder services fee (Note 4)		676,444
Administration fee (Note 3)		338,222
Transfer agent fees and expenses		94,992
Professional fees		36,135
Custodian Fees		24,248
Trustees’ fees and expenses		18,245
Shareholder reports and notices		14,003
Registration fees		9,383
Other		10,352
Total Expenses		3,741,766
Less: amounts waived/reimbursed (Note 4)		(2,902,352	)
Less: rebate from Morgan Stanley affiliated cash sweep (Note 5)		(681	)
Net Expenses		838,733
Net Investment Income		68,314
Net Realized Gain		5,295
Net Increase	$	73,609

See Notes to Financial Statements

16

Morgan Stanley New York Municipal Money Market Trust

Financial Statements  continued

Statements of Changes in Net Assets

	FOR THE SIX MONTHS ENDED JUNE 30, 2013			FOR THE YEAR ENDED DECEMBER 31, 2012
	(unaudited)
Increase (Decrease) in Net Assets:
Operations:
Net investment income	$	68,314		$	140,955
Net realized gain		5,295			33,297
Net Increase		73,609			174,252
Dividends to Shareholders from Net Investment Income:
Class R shares		(19,608	)		(45,266	)
Class S shares		(48,031	)		(95,728	)
Total Dividends		(67,639	)		(140,994	)
Net decrease from transactions in shares of beneficial interest		(87,938,782	)		(40,429,136	)
Net Decrease		(87,932,812	)		(40,395,878	)
Net Assets:
Beginning of period		1,392,460,278			1,432,856,156
End of Period
(Including dividends in excess of net investment income of $(23,374) and $(24,049), respectively)	$	1,304,527,466		$	1,392,460,278

See Notes to Financial Statements

17

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial StatementsⁿJune 30, 2013 (unaudited)

1. Organization and Accounting Policies

Morgan Stanley New York Municipal Money Market Trust (the “Fund”), is registered under the Investment Company Act of 1940, as amended (the “Act”), as a diversified, open-end management investment company. The Fund’s investment objective is to seek a high level of daily income which is exempt from federal and New York income tax, consistent with stability of principal and liquidity. The Fund was organized as a Massachusetts business trust on December 28, 1989 and commenced operations on March 20, 1990.

The Fund offers two classes of shares, the Reserve Class (“Class R”) and the AA Sweep Class (“Class S”). Class R shares are offered to the general public and Class S shares are offered exclusively to investors who have an Active Assets Account with Morgan Stanley Wealth Management, an affiliate of Morgan Stanley Investment Management Inc. (the “Adviser”). The two classes have the same fees and expenses.

The following is a summary of significant accounting policies:

A. Valuation of Investments — Portfolio securities are valued at amortized cost, which approximates fair value, in accordance with Rule 2a-7 under the Act. Investments in mutual funds, including the Morgan Stanley Institutional Liquidity Funds, are valued at the net asset value as of the close of each business day.

B. Accounting for Investments — Security transactions are accounted for on the trade date (date the order to buy or sell is executed). Realized gains and losses on security transactions are determined by the identified cost method. Discounts are accreted and premiums are amortized over the life of the respective securities and are included in interest income. Interest income is accrued daily as earned.

C. Multiple Class Allocations — Investment income, expenses (other than distribution fees), and realized and unrealized gains and losses are allocated to each class of shares based upon the relative net asset value on the date such items are recognized. Distribution fees are charged directly to the respective class.

D. Dividends and Distributions to Shareholders — Dividends and distributions to shareholders are recorded on the close of each business day.

E. Use of Estimates — The preparation of financial statements in accordance with generally accepted accounting principles in the United States (“GAAP”) requires management to make estimates and assumptions that affect the reported amounts and disclosures. Actual results could differ from those estimates.

F. Indemnifications — The Fund enters into contracts that contain a variety of indemnifications. The Fund’s maximum exposure under these arrangements is unknown. However, the Fund has not had prior claims or losses pursuant to these contracts and expects the risk of loss to be remote.

18

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial StatementsⁿJune 30, 2013 (unaudited)  continued

2. Fair Valuation Measurements

Financial Accounting Standards Board (“FASB”) Accounting Standards Codification (“ASC”) 820, Fair Value Measurements and Disclosures (“ASC 820”), defines fair value as the value that the Fund would receive to sell an investment or pay to transfer a liability in a timely transaction with an independent buyer in the principal market, or in the absence of a principal market the most advantageous market for the investment or liability. ASC 820 establishes a three-tier hierarchy to distinguish between (1) inputs that reflect the assumptions market participants would use in valuing an asset or liability developed based on market data obtained from sources independent of the reporting entity (observable inputs); and (2) inputs that reflect the reporting entity’s own assumptions about the assumptions market participants would use in valuing an asset or liability developed based on the best information available in the circumstances (unobservable inputs) and to establish classification of fair value measurements for disclosure purposes. Various inputs are used in determining the value of the Fund’s investments. The inputs are summarized in the three broad levels listed below.

• Level 1 — unadjusted quoted prices in active markets for identical investments

• Level 2 — other significant observable inputs (including quoted prices for similar investments, interest rates, prepayment speeds, credit risk, etc.)

• Level 3 — significant unobservable inputs including the Fund’s own assumptions in determining the fair value of investments. Factors considered in making this determination may include, but are not limited to, information obtained by contacting the issuer, analysts, or the appropriate stock exchange (for exchange-traded securities), analysis of the issuer’s financial statements or other available documents and, if necessary, available information concerning other securities in similar circumstances

The inputs or methodology used for valuing securities are not necessarily an indication of the risk associated with investing in those securities and the determination of the significance of a particular input to the fair value measurement in its entirety requires judgment and considers factors specific to each security.

The following is a summary of the inputs used to value the Fund’s investments as of June 30, 2013.

INVESTMENT TYPE	LEVEL 1 UNADJUSTED QUOTED PRICES		LEVEL 2 OTHER SIGNIFICANT OBSERVABLE INPUTS		LEVEL 3 SIGNIFICANT UNOBSERVABLE INPUTS		TOTAL
Assets:
Weekly Variable Rate Bonds	$	—	$	955,703,000	$	—	$	955,703,000
Daily Variable Rate Bonds		—		128,925,000		—		128,925,000
Municipal Bonds & Notes		—		86,134,658		—		86,134,658
Commercial Paper		—		69,805,000		—		69,805,000
Closed-End Investment Companies		—		36,500,000		—		36,500,000
Put Option Bond		—		29,000,000		—		29,000,000
Total Assets	$	—	$	1,306,067,658	$	—	$	1,306,067,658

19

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial StatementsⁿJune 30, 2013 (unaudited)  continued

Transfers between investment levels may occur as the markets fluctuate and/or the availability of data used in an investment’s valuation changes. The Fund recognizes transfers between the levels as of the end of the period. As of June 30, 2013, the Fund did not have any investments transfer between investment levels.

3. Advisory/Administration Agreements

Pursuant to an Investment Advisory Agreement with the Adviser, the Fund pays the Adviser an advisory fee, accrued daily and payable monthly, by applying the following annual rates to the net assets of the Fund determined as of the close of each business day: 0.45% to the portion of the daily net assets not exceeding $500 million; 0.375% to the portion of the daily net assets exceeding $500 million but not exceeding $750 million; 0.325% to the portion of the daily net assets exceeding $750 million but not exceeding $1 billion; 0.30% to the portion of the daily net assets exceeding $1 billion but not exceeding $1.5 billion; 0.275% to the portion of the daily net assets exceeding $1.5 billion but not exceeding $2 billion; 0.25% to the portion of the daily net assets exceeding $2 billion but not exceeding $2.5 billion; 0.225% to the portion of the daily net assets exceeding $2.5 billion but not exceeding $3 billion; and 0.20% to the portion of the daily net assets exceeding $3 billion. For the six months ended June 30, 2013, the advisory fee rate (net of waivers/rebate) was equivalent to an annual effective rate of 0.04% of the Fund’s daily net assets.

Pursuant to an Administration Agreement with Morgan Stanley Services Company Inc. (the “Administrator”), an affiliate of the Adviser, the Fund pays an administration fee, accrued daily and payable monthly, by applying the annual rate of 0.05% to the Fund’s daily net assets.

Under a Sub-Administration Agreement between the Administrator and State Street Bank and Trust Company (“State Street”), State Street provides certain administrative services to the Fund. For such services, the Administrator pays State Street a portion of the fee the Administrator receives from the Fund.

The Fund’s Adviser and Administrator have agreed to assume all operating expenses of the Fund and to waive the advisory fee and administrative fee, as applicable, to the extent that such expenses and fees excluding certain investment related expenses, taxes, interest and other extraordinary expenses (including litigation), on an annualized basis exceeds 0.60% of the average daily net assets of the Fund. These fee waivers and/or expense reimbursements will continue for at least one year or until such time that the Fund’s Board of Trustees, (the “Trustees”), act to discontinue all or a portion of such waivers and/or expense reimbursements when it deems such action is appropriate.

4. Shareholder Services Plan

Pursuant to a Shareholder Services Plan (the “Plan”), the Fund may pay Morgan Stanley Distribution, Inc. (the “Distributor”) as compensation for the provision of services to shareholders a service fee up to the rate of 0.15% on an annualized basis of the average daily net assets of the Fund.

20

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial StatementsⁿJune 30, 2013 (unaudited)  continued

Reimbursements for these expenses are made in monthly payments by the Fund to the Distributor, which will in no event exceed an amount equal to a payment at the annual rate of 0.15% of the Fund’s average daily net assets during the month. Expenses incurred by the Distributor pursuant to the Plan in any fiscal year will not be reimbursed by the Fund through payments accrued in any subsequent fiscal year. For the six months ended June 30, 2013, the distribution fee was accrued at the annual rate of 0.10%.

The Distributor, Adviser and Administrator have agreed to waive and/or reimburse all or a portion of the Fund’s shareholder services fee, advisory fee and administration fee, respectively, to the extent that total expenses exceed total income of the Fund on a daily basis. For the six months ended June 30, 2013, the Distributor waived $676,444 and the Adviser waived $2,225,908. These fee waivers and/or expense reimbursements will continue for at least one year or until such time that the Trustees act to discontinue all or a portion of such waivers and/or expense reimbursements when it deems such action is appropriate.

5. Transactions with Affiliates

The Fund invests in the Institutional Class of the Morgan Stanley Institutional Liquidity Funds — Government Portfolio (the “Liquidity Funds”), an open-end management investment company managed by the Adviser. Advisory fees paid by the Fund are reduced by an amount equal to its pro-rata share of the advisory and administration fees paid by the Fund due to its investment in the Liquidity Funds. For the six months ended June 30, 2013, advisory fees paid were reduced by $681 relating to the Fund’s investment in the Liquidity Funds.

A summary of the Fund’s transactions in shares of the Liquidity Funds during the six months ended June 30, 2013 is as follows:

VALUE DECEMBER 31, 2012	PURCHASES AT COST		SALES	DIVIDEND INCOME	VALUE JUNE 30, 2013
—	$	59,250,000	$59,250,000	$234	—

Morgan Stanley Services Company Inc., an affiliate of the Adviser and Distributor, was the Fund’s transfer agent. Effective July 1, 2013, the Trustees approved changing the transfer agent to Boston Financial Data Services, Inc.

The Fund has an unfunded noncontributory defined benefit pension plan covering certain independent Trustees of the Fund who will have served as independent Trustees for at least five years at the time of retirement. Benefits under this plan are based on factors which include years of service and compensation. The Trustees voted to close the plan to new participants and eliminate the future benefits growth due to increases to compensation after July 31, 2003. Aggregate pension costs for the six months ended June 30, 2013, included in “Trustees’ fees and expenses” in the Statement of Operations amounted to $2,463. At June 30, 2013, the Fund had an accrued pension liability of $59,374, which is included in “Accrued expenses and other payables” in the Statement of Assets and Liabilities.

21

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial StatementsⁿJune 30, 2013 (unaudited)  continued

The Fund has an unfunded Deferred Compensation Plan (the “Compensation Plan”), which allows each independent Trustee to defer payment of all, or a portion, of the fees they receive for serving on the Board of Trustees. Each eligible Trustee generally may elect to have the deferred amounts credited with a return equal to the total return on one or more of the Morgan Stanley funds that are offered as investment options under the Compensation Plan. Appreciation/depreciation and distributions received from these investments are recorded with an offsetting increase/decrease in the deferred compensation obligation and do not affect the net asset value of the Fund.

6. Shares of Beneficial Interest

Transactions in shares of beneficial interest, at $1.00 per share, were as follows:

	FOR THE SIX MONTHS ENDED JUNE 30, 2013			FOR THE YEAR ENDED DECEMBER 31, 2012
	(unaudited)
CLASS R SHARES
Shares sold		459,092,583			1,407,317,491
Shares issued in reinvestment of dividends		19,608			44,845
Shares redeemed		(515,986,638	)		(1,469,154,862	)
Net decrease – Class R		(56,874,447	)		(61,792,526	)
CLASS S SHARES
Shares sold		1,471,842,417			2,814,831,091
Shares issued in reinvestment of dividends		48,031			95,728
Shares redeemed		(1,502,954,783	)		(2,793,563,429	)
Net increase (decrease) – Class S		(31,064,335	)		21,363,390
Net decrease in Fund		(87,938,782	)		(40,429,136	)

7. Federal Income Tax Status

It is the Fund’s intention to continue to qualify as a regulated investment company and distribute all of its taxable and tax-exempt income. Accordingly, no provision for Federal income taxes is required in the financial statements.

Dividend income and distributions to shareholders are recorded on the ex-dividend date. Interest income is recognized on an accrual basis. Dividends from net investment income, if any, are declared and paid daily. Net realized capital gains, if any, are distributed at least annually.

FASB ASC 740-10, Income Taxes — Overall, sets forth a minimum threshold for financial statement recognition of the benefit of a tax position taken or expected to be taken in a tax return. Management has concluded there are no significant uncertain tax positions that would require recognition in the financial

statements. If applicable, the Fund recognizes interest accrued related to unrecognized tax benefits in

22

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial StatementsⁿJune 30, 2013 (unaudited)  continued

“Interest Expense” and penalties in ‘‘Other Expenses” in the Statement of Operations. The Fund files tax returns with the U.S. Internal Revenue Service, New York and various states. Each of the tax years in the four-year period ended December 31, 2012, remains subject to examination by taxing authorities.

The tax character of distributions paid may differ from the character of distributions shown in the Statements of Changes in Net Assets due to short-term capital gains being treated as ordinary income for tax purposes. The tax character of distributions paid during fiscal years 2012 and 2011 was as follows:

2012 DISTRIBUTIONS PAID FROM:			2011 DISTRIBUTIONS PAID FROM:
TAX-EXEMPT INCOME	ORDINARY INCOME	LONG-TERM CAPITAL GAIN	TAX-EXEMPT INCOME	ORDINARY INCOME	LONG-TERM CAPITAL GAIN
$111,340	$19,006	$10,648	$109,163	$135	—

The amount and character of income and gains to be distributed are determined in accordance with income tax regulations which may differ from GAAP. These book/tax differences are either considered temporary or permanent in nature.

Temporary differences are attributable to differing book and tax treatments for the timing of the recognition of gains (losses) on certain investment transactions and the timing of the deductibility of certain expenses.

Permanent differences, primarily due to a distribution reclass, equalization and nondeductible expenses, resulted in the following reclassifications among the Fund’s components of net assets at December 31, 2012:

DIVIDENDS IN EXCESS OF NET INVESTMENT INCOME	ACCUMULATED UNDISTRIBUTED NET REALIZED GAIN	PAID-IN-CAPITAL
$30,745	$(51,934)	$21,189

At December 31, 2012, the components of distributable earnings for the Fund on a tax basis were as follows:

UNDISTRIBUTED ORDINARY INCOME	UNDISTRIBUTED TAX-EXEMPT INCOME	UNDISTRIBUTED LONG-TERM CAPITAL GAIN
—	$44,687	—

At June 30, 2013, the aggregate cost for federal income tax purposes is the same as the cost for book purposes.

On December 22, 2010, the Regulated Investment Company Modernization Act of 2010 (the “Modernization Act”) was signed into law. The Modernization Act modernizes several tax provisions related to Regulated Investment Companies (“RICs”) and their shareholders. One key change made by the Modernization Act is that capital losses will generally retain their character as short-term or long-term and may be carried forward indefinitely to offset future gains. These losses are utilized before other capital loss carryforwards that expire. Generally, the Modernization Act is effective for taxable years beginning after December 22, 2010.

23

Morgan Stanley New York Municipal Money Market Trust

Financial Highlights

Selected ratios and per share data for a share of beneficial interest outstanding throughout each period:

	FOR THE SIX MONTHS ENDED JUNE 30, 2013			FOR THE YEAR ENDED DECEMBER 31,
				2012			2011			2010^			2009^			2008^
	(unaudited)
Class R Shares
Selected Per Share Data:
Net asset value, beginning of period		$1.00			$1.00			$1.00			$1.00			$1.00			$1.00
Net income from investment operations		0.000	(1)		0.000	(1)		0.000	(1)		0.000	(1)		0.000	(1)		0.015
Less dividends from net investment income		(0.000	)(1)		(0.000	)(1)		(0.000	)(1)		(0.000	)(1)		(0.000	)(1)		(0.015	)(2)
Net asset value, end of period		$1.00			$1.00			$1.00			$1.00			$1.00			$1.00
Total Return		0.00	%(6)(7)		0.01	%		0.01	%		0.01	%		0.04	%		1.54	%
Ratios to Average Net Assets(3):
Net expenses		0.12	%(4)(8)		0.15	%(4)		0.13	%(4)		0.30	%(4)		0.52	%(4)(5)		0.62	%(4)(5)
Net investment income		0.01	%(4)(8)		0.01	%(4)		0.01	%(4)		0.00	%(4)(6)		0.05	%(4)(5)		1.43	%(4)(5)
Rebate from Morgan Stanley affiliate		0.00	%(6)(8)		0.00	%(6)		0.00	%(6)		0.00	%(6)		0.00	%(6)		0.02	%
Supplemental Data:
Net assets, end of period, in thousands		$361,674			$418,547			$480,329			$31,242			$38,226			$70,716

^ Beginning with the year ended December 31, 2011, the Fund was audited by Ernst & Young LLP. The previous years were audited by another independent registered public accounting firm.

(1) Amount is less than $0.001.

(2) Includes a long-term capital gain distribution of less than $0.001.

(3) If the Fund had borne all of its expenses that were reimbursed or waived by the Distributor, Adviser and Administrator, the annualized expense and net investment income (loss) ratios, would have been as follows:

PERIOD ENDED	EXPENSE RATIO			NET INVESTMENT INCOME (LOSS) RATIO
June 30, 2013		0.55	%		(0.42	)%
December 31, 2012		0.57			(0.41	)
December 31, 2011		0.55			(0.41	)
December 31, 2010		0.69			(0.39	)
December 31, 2009		0.74			(0.17	)
December 31, 2008		0.65			1.40

(4) The ratios reflect the rebate of certain Fund expenses in connection with investments in a Morgan Stanley affiliate during the period. The effect of the rebate on the ratios is disclosed in the above table as “Rebate from Morgan Stanley affiliate.”

(5) Reflects fees paid in connection with the U.S. Treasury’s Temporary Guarantee Program for Money Market Funds. This fee had an effect of 0.07% and 0.02% for the years ended 2009 and 2008, respectively.

(6) Amount is less than 0.005%.

(7) Not annualized.

(8) Annualized.

See Notes to Financial Statements

24

Morgan Stanley New York Municipal Money Market Trust

Financial Highlights  continued

	FOR THE SIX MONTHS ENDED JUNE 30, 2013			FOR THE YEAR ENDED DECEMBER 31,
				2012			2011			2010^			2009^			2008^
	(unaudited)
Class S Shares
Selected Per Share Data:
Net asset value, beginning of period		$1.00			$1.00			$1.00			$1.00			$1.00			$1.00
Net income from investment operations		0.000	(1)		0.000	(1)		0.000	(1)		0.000	(1)		0.000	(1)		0.015
Less dividends from net investment income		(0.000	)(1)		(0.000	)(1)		(0.000	)(1)		(0.000	)(1)		(0.000	)(1)		(0.015	)(2)
Net asset value, end of period		$1.00			$1.00			$1.00			$1.00			$1.00			$1.00
Total Return		0.00	%(6)(7)		0.01	%		0.01	%		0.01	%		0.04	%		1.54	%
Ratios to Average Net Assets(3):
Net expenses		0.12	%(4)(8)		0.15	%(4)		0.13	%(4)		0.30	%(4)		0.52	%(4)(5)		0.62	%(4)(5)
Net investment income		0.01	%(4)(8)		0.01	%(4)		0.01	%(4)		0.00	%(4)(6)		0.05	%(4)(5)		1.43	%(4)(5)
Rebate from Morgan Stanley affiliate		0.00	%(6)(8)		0.00	%(6)		0.00	%(6)		0.00	%(6)		0.00	%(6)		0.02	%
Supplemental Data:
Net assets, end of period, in thousands		$942,853			$973,913			$952,527			$143,694			$177,412			$486,311

^ Beginning with the year ended December 31, 2011, the Fund was audited by Ernst & Young LLP. The previous years were audited by another independent registered public accounting firm.

(1) Amount is less than $0.001.

(2) Includes a long-term capital gain distribution of less than $0.001.

(3) If the Fund had borne all of its expenses that were reimbursed or waived by the Distributor, Adviser and Administrator, the annualized expense and net investment income (loss) ratios, would have been as follows:

PERIOD ENDED	EXPENSE RATIO			NET INVESTMENT INCOME (LOSS) RATIO
June 30, 2013		0.55	%		(0.42	)%
December 31, 2012		0.57			(0.41	)
December 31, 2011		0.55			(0.41	)
December 31, 2010		0.69			(0.39	)
December 31, 2009		0.74			(0.17	)
December 31, 2008		0.65			1.40

(4) The ratios reflect the rebate of certain Fund expenses in connection with investments in a Morgan Stanley affiliate during the period. The effect of the rebate on the ratios is disclosed in the above table as “Rebate from Morgan Stanley affiliate.”

(5) Reflects fees paid in connection with the U.S. Treasury’s Temporary Guarantee Program for Money Market Funds. This fee had an effect of 0.07% and 0.02% for the years ended 2009 and 2008, respectively.

(6) Amount is less than 0.005%.

(7) Not annualized.

(8) Annualized.

See Notes to Financial Statements

25

Morgan Stanley New York Municipal Money Market Trust

U.S. Privacy Policy (unaudited)

An Important Notice Concerning Our U.S. Privacy Policy

This privacy notice describes the U.S. privacy policy of Morgan Stanley Distribution, Inc., and the Morgan Stanley family of mutual funds (“us”, “our”, “we”).

We are required by federal law to provide you with notice of our U.S. privacy policy (“Policy”). This Policy applies to both our current and former clients unless we state otherwise and is intended for individual clients who purchase products or receive services from us for personal, family or household purposes. This Policy is not applicable to partnerships, corporations, trusts or other non-individual clients or account holders, nor is this Policy applicable to individuals who are either beneficiaries of a trust for which we serve as trustee or participants in an employee benefit plan administered or advised by us. This Policy is, however, applicable to individuals who select us to be a custodian of securities or assets in individual retirement accounts, 401(k) accounts, or accounts subject to the Uniform Gifts to Minors Act.

This notice sets out our business practices to protect your privacy; how we collect and share personal information about you; and how you can limit our sharing or certain uses by others of this information. We may amend this Policy at any time, and will inform you of any changes to our Policy as required by law.

We Respect Your Privacy

We appreciate that you have provided us with your personal financial information and understand your concerns about your information. We strive to safeguard the information our clients entrust to us. Protecting the confidentiality and security of client information is an important part of how we conduct our business.

This notice describes what personal information we collect about you, how we collect it, when we may share it with others, and how certain others may use it. It discusses the steps you may take to limit our sharing of certain information about you with our affiliated companies, including, but not limited to our affiliated banking businesses, brokerage firms and credit service affiliates. It also discloses how you may limit our affiliates’ use of shared information for marketing purposes.

Throughout this Policy, we refer to the nonpublic information that personally identifies you as “personal information.” We also use the term “affiliated company” in this notice. An affiliated company is a company in our family of companies and includes companies with the Morgan Stanley name. These affiliated companies are financial institutions such as broker-dealers, banks, investment advisers and credit card issuers. We refer to any company that is not an affiliated company as a nonaffiliated third party. For purposes of Section 5 of this notice, and your ability to limit certain uses of personal information by our affiliates, this notice applies to the use of personal information by our affiliated companies.

26

Morgan Stanley New York Municipal Money Market Trust

U.S. Privacy Policy (unaudited)  continued

1.  What Personal Information Do We Collect From You?

We may collect the following types of information about you: (i) information provided by you, including information from applications and other forms we receive from you, (ii) information about your transactions with us or our affiliates, (iii) information about your transactions with nonaffiliated third parties, (iv) information from consumer reporting agencies, (v) information obtained from our websites, and (vi) information obtained from other sources. For example:

• We collect information such as your name, address, e-mail address, telephone/fax numbers, assets, income and investment objectives through applications and other forms you submit to us.

• We may obtain information about account balances, your use of account(s) and the types of products and services you prefer to receive from us through your dealings and transactions with us and other sources.

• We may obtain information about your creditworthiness and credit history from consumer reporting agencies.

• We may collect background information from and through third-party vendors to verify representations you have made and to comply with various regulatory requirements.

2.  When Do We Disclose Personal Information We Collect About You?

We may disclose personal information we collect about you in each of the categories listed above to affiliated and nonaffiliated third parties.

a. Information We Disclose to Affiliated Companies.    We may disclose personal information that we collect about you to our affiliated companies to manage your account(s) effectively, to service and process your transactions, and to let you know about products and services offered by us and affiliated companies, to manage our business, and as otherwise required or permitted by law. Offers for products and services from affiliated companies are developed under conditions designed to safeguard your personal information.

b. Information We Disclose to Third Parties.    We may disclose personal information that we collect about you to nonaffiliated third parties to provide marketing services on our behalf or to other financial institutions with whom we have joint marketing agreements. We may also disclose all of the information we collect to other nonaffiliated third parties for our everyday business purposes, such as to process transactions, maintain account(s), respond to court orders and legal investigations, report to credit bureaus, offer our own products and services, protect against fraud, for institutional risk control, to perform services on our behalf, and as otherwise required or permitted by law.

When we share personal information about you with a nonaffiliated third party, they are required to limit their use of personal information about you to the particular purpose for which it was shared and they are not allowed to share personal information about you with others except to fulfill that limited purpose or as may be permitted or required by law.

27

Morgan Stanley New York Municipal Money Market Trust

U.S. Privacy Policy (unaudited)  continued

3.  How Do We Protect The Security and Confidentiality Of Personal Information We Collect About You?

We maintain physical, electronic and procedural security measures that comply with applicable law and regulations to help safeguard the personal information we collect about you. We have internal policies governing the proper handling of client information by employees. Third parties that provide support or marketing services on our behalf may also receive personal information about you, and we require them to adhere to appropriate security standards with respect to such information.

4.  How Can You Limit Our Sharing Certain Personal Information About You With Our Affiliated Companies For Eligibility Determination?

By following the opt-out procedures in Section 6 below, you may limit the extent to which we share with our affiliated companies, personal information that was collected to determine your eligibility for products and services such as your credit reports and other information that you have provided to us or that we may obtain from third parties (“eligibility information”). Eligibility information does not include your identification information or personal information pertaining to our transactions or experiences with you. Please note that, even if you direct us not to share eligibility information with our affiliated companies, we may still share your personal information, including eligibility information, with our affiliated companies under circumstances that are permitted under applicable law, such as to process transactions or to service your account.

5.  How Can You Limit the Use of Certain Personal Information About You by Our Affiliated Companies for Marketing?

By following the opt-out instructions in Section 6 below, you may limit our affiliated companies from marketing their products or services to you based on personal information we disclose to them. This information may include, for example, your income and account history with us. Please note that, even if you choose to limit our affiliated companies from using personal information about you that we may share with them for marketing their products and services to you, our affiliated companies may use your personal information that they obtain from us to market to you in circumstances permitted by law, such as if the affiliated party has its own relationship with you.

6.  How Can You Send Us an Opt-Out Instruction?

If you wish to limit our sharing of eligibility information about you with our affiliated companies, or our affiliated companies’ use of personal information for marketing purposes, as described in this notice, you may do so by:

• Calling us at (800) 548-7786

Monday–Friday between 8a.m. and 5p.m. (EST)

28

Morgan Stanley New York Municipal Money Market Trust

U.S. Privacy Policy (unaudited)  continued

• Writing to us at the following address:

Boston Financial Data Services, Inc.

c/o Privacy Coordinator

P.O. Box 219804

Kansas City, Missouri 64121

If you choose to write to us, your request should include: your name, address, telephone number and account number(s) to which the opt-out applies and whether you are opting out with respect to sharing of eligibility information (Section 4 above), or information used for marketing (Section 5 above), or both. Written opt-out requests should not be sent with any other correspondence. In order to process your request, we require that the request be provided by you directly and not through a third party. Once you have informed us about your privacy preferences, your opt-out preference will remain in effect with respect to this Policy (as it may be amended) until you notify us otherwise. If you are a joint account owner, we will accept instructions from any one of you and apply those instructions to the entire account.

Please understand that if you limit our sharing or our affiliated companies’ use of personal information, you and any joint account holder(s) may not receive information about our affiliated companies’ products and services, including products or services that could help you manage your financial resources and achieve your investment objectives.

If you have more than one account or relationship with us, please specify the accounts to which you would like us to apply your privacy choices. If you have accounts or relationships with our affiliates, you may receive multiple privacy policies from them, and will need to separately notify those companies of your privacy choices for those accounts or relationships.

7.  What if an affiliated company becomes a nonaffiliated third party?

If, at any time in the future, an affiliated company becomes a nonaffiliated third party, further disclosures of personal information made to the former affiliated company will be limited to those described in Section 2(b) above relating to nonaffiliated third parties. If you elected under Section 6 to limit disclosures we make to affiliated companies, or use of personal information by affiliated companies, your election will not apply to use by any former affiliated company of your personal information in their possession once it becomes a nonaffiliated third party.

29

Morgan Stanley New York Municipal Money Market Trust

U.S. Privacy Policy (unaudited)  continued

Special Notice to Residents of Vermont

The following section supplements our Policy with respect to our individual clients who have a Vermont address and supersedes anything to the contrary in the above Policy with respect to those clients only.

The State of Vermont requires financial institutions to obtain your consent prior to sharing personal information that they collect about you with nonaffiliated third parties, or eligibility information with affiliated companies, other than in certain limited circumstances. Except as permitted by law, we will not share personal information we collect about you with nonaffiliated third parties or eligibility information with affiliated companies, unless you provide us with your written consent to share such information.

Special Notice to Residents of California

The following section supplements our Policy with respect to our individual clients who have a California address and supersedes anything to the contrary in the above Policy with respect to those clients only.

In response to a California law, if your account has a California home address, your personal information will not be disclosed to nonaffiliated third parties except as permitted by applicable California law, and we will limit sharing such personal information with our affiliates to comply with California privacy laws that apply to us.

30

Item 2. Code of Ethics.

Not applicable for semiannual reports.

Item 3. Audit Committee Financial Expert.

Not applicable for semiannual reports.

Item 4. Principal Accountant Fees and Services

Not applicable for semiannual reports.

Item 5. Audit Committee of Listed Registrants.

Not applicable for semiannual reports.

Item 6.

(a) Refer to Item 1.

(b) Not applicable.

Item 7. Disclosure of Proxy Voting Policies and Procedures for Closed-End Management Investment Companies.

Not applicable for semiannual reports.

Item 8. Portfolio Managers of Closed-End Management Investment Companies

Applicable only to annual reports filed by closed-end funds.

Item 9. Closed-End Fund Repurchases

Applicable to reports filed by closed-end funds.

Item 10. Submission of Matters to a Vote of Security Holders

Not applicable.

Item 11. Controls and Procedures

(a) The Fund’s principal executive officer and principal financial officer have concluded that the Fund’s disclosure controls and procedures are sufficient to ensure that information required to be disclosed by the Fund in this Form N-CSR was recorded, processed, summarized and reported within the time periods specified in the Securities and Exchange Commission’s rules and forms, based upon such officers’ evaluation of these controls and procedures as of a date within 90 days of the filing date of the report.

(b) There were no changes in the registrant’s internal control over financial reporting that occurred during the second fiscal quarter of the period covered by this report that has materially affected, or is reasonably likely to materially affect, the registrant’s internal control over financial reporting.

Item 12. Exhibits

(a) Code of Ethics – Not applicable for semiannual reports.

(b) A separate certification for each principal executive officer and principal financial officer of the registrant are attached hereto as part of EX-99.CERT.

2

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Morgan Stanley New York Municipal Money Market Trust

/s/ Kevin Klingert

Kevin Klingert

Principal Executive Officer

August 15, 2013

Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, this report has been signed by the following persons on behalf of the registrant and in the capacities and on the dates indicated.

/s/ Kevin Klingert

Kevin Klingert

Principal Executive Officer

August 15, 2013

/s/ Francis Smith

Francis Smith

Principal Financial Officer

August 15, 2013

3