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)

Randy Takian
522 Fifth Avenue, New York, New York 10036
(Name and address of agent for service)

Registrant’s telephone number, including area code: 212-296-6990

Date of fiscal year end: December 31

Date of reporting period: June 30, 2010

Item 1 — Report to Shareholders

INVESTMENT MANAGEMENT

Welcome, Shareholder:

In this report, you’ll learn about how your investment in Morgan Stanley New York Municipal Money Market Trust performed during the semiannual period. We will provide an overview of the market conditions, and discuss some of the factors that affected performance during the reporting period. In addition, this report includes the Fund’s financial statements and a list of Fund investments.

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.

Fund Report

For the six months ended June 30, 2010

Market Conditions

Overall, conditions in the tax-exempt money market have improved in recent months. Demand for variable rate demand notes (or VRDNs, which represent the majority of short-term tax-exempt instruments) has been strong due to the attractive relative value of these securities versus Treasury bills. In the first six months of 2010, yields on weekly VRDNs, as measured by the Securities Industry and Financial Markets Association (SIFMA) Index, averaged 100 percent of yields on comparable taxable issues.

Recently, we have seen more issuers coming to market with one-year notes, which served to increase overall supply in the market and cause credit spreads to widen. Additionally, we have seen a bifurcated market as municipal issuers with stellar credit have benefited by issuing debt at very attractive rates while issuers who have been hit harder by the economic downturn are paying higher rates for their short-term financing.

For the first time since the outset of the recession, state governments saw year-over-year tax collections rise in the first quarter of 2010, but revenues were still well below pre-recession levels for most states. According to an analysis of Census Bureau data released by the Nelson A. Rockefeller Institute of Government at the State University of New York, state tax revenues increased 2.5 percent to $164.5 billion during the quarter, but much of this increase came from two states, California and New York, that have raised taxes in an attempt to close budget gaps. The Institute’s report also noted that data from the 42 states that have released tax figures for April and May of this year suggests revenues for the second quarter grew less than one percent. With tax revenues still lagging and the phasing out of state assistance that was part of the federal economic stimulus plan, state budgets are expected to be under strain for several years.

The New York State economy is still reeling from the broad-based recession that engulfed both Wall Street and Main Street, though conditions are expected to improve during the current year. The state faces continuing budget shortfalls and some of the revenues it was depending on are in serious doubt. According to many estimates, New York State’s cumulative budget deficit is forecast to exceed $50 billion by as early as 2012 unless, according to the Governor, austere cuts are made to spending on health care, public education, salaries and benefits to public workers, and other programs that benefit working people.

Performance Analysis

As of June 30, 2010, Morgan Stanley New York Municipal Money Market Trust had net assets of approximately $211 million and an average portfolio maturity of 15 days. For the six-month period ended June 30, 2010, 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, 2010, the Fund’s Class R and Class S shares provided an effective annualized yield of 0.01 percent (subsidized) and –0.34 percent (non-subsidized) and a current yield of 0.01 percent (subsidized) and –0.34 percent (non-subsidized), while its 30-day moving average yield for June was 0.01 percent (subsidized) and –0.33 percent (non-subsidized). Yield quotations more closely reflect the current earnings of the Fund.

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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.

Protecting the safety and liquidity of the Fund’s assets remained our first priority throughout the reporting period. To that end, we have focused on tax-exempt securities where our credit and risk teams have confidence in the quality of the issuer, the structure of the program, and the financial strength of the supporting institutions. In particular, investments have focused on issues with direct revenue streams such as water and sewer bonds. Furthermore, we continued to maintain a high level of liquidity in the portfolio with weighted average maturities on the short end of the maturity spectrum.

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 06/30/10
Variable Rate Municipal Obligations	88	.5%
Tax-Exempt Commercial Paper	6	.1
Municipal Notes and Bonds	5	.4

MATURITY SCHEDULE as of 06/30/10
1 – 30 Days	90.4	%
31 – 60 Days	4.9
61 – 90 Days	—
91 – 120 Days	—
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.

3

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 Investment Adviser 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. Morgan Stanley does not deliver the reports for the first and third fiscal quarters to shareholders, nor are the reports posted to the Morgan Stanley public web site. You may, however, obtain the Form N-Q filings (as well as the Form N-CSR and N-CSRS 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.

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Expense Example

As a shareholder of the Fund, you incur ongoing costs, including advisory fees; distribution and shareholder servicing 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.

The example is based on an investment of $1,000 invested at the beginning of the period and held for the entire period 01/01/10 – 06/30/10.

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		Ending		Expenses Paid
	Account Value		Account Value		During Period@
					01/01/10 –
	01/01/10		06/30/10		06/30/10
Class R
Actual (0.00% return)	$	1,000.00	$	1,000.00	$	1.64
Hypothetical (5% annual return before expenses)	$	1,000.00	$	1,023.16	$	1.66
Class S
Actual (0.00% return)	$	1,000.00	$	1,000.00	$	1.64
Hypothetical (5% annual return before expenses)	$	1,000.00	$	1,023.16	$	1.66

@ Expenses are equal to the Fund’s annualized expense ratios of 0.33% and 0.33% for Class R and Class S shares, respectively, multiplied by the average account value over the period, multiplied by 181/365 (to reflect the one-half year period). If the Fund had borne all of its expenses, the annualized expense ratios would have been 0.70% and 0.70% for Class R and Class S shares, respectively.

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Investment Advisory Agreement Approval

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, 2009, as applicable). When a fund underperforms its benchmark and/or its peer group average, the Board and the Adviser 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 one-, three- and five-year periods. 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 advised by the Adviser and 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 while the Fund’s management fee was higher than its peer group average, the total expense ratio was lower than its peer group average. After

6

discussion, the Board concluded that (i) the Fund’s performance was acceptable, (ii) the Fund’s management fee, although higher than its peer group average, was acceptable given the quality and nature of services provided, and (iii) the Fund’s total expense ratio was competitive with its peer group average.

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

7

policies and procedures formulated and adopted by the Adviser for managing the Fund’s operations and the 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.

8

Morgan Stanley New York Municipal Money Market Trust

Portfolio of Investments - June 30, 2010 (unaudited)

PRINCIPAL
AMOUNT IN			COUPON				DEMAND
THOUSANDS			RATE (a)				DATE (b)	VALUE
		New York Tax-Exempt Short-Term Variable Rate Municipal Obligations (88.5%)
		Austin Trust,
$	2,750	New York City Municipal Water Finance Authority Fiscal 2009 Ser CC Custody Receipts Ser 2008-1192		0	.31	%	07/07/10	$	2,750,000
	2,200	New York City Municipal Water Finance Authority Second General Fiscal 2007 Ser DD Custody Receipts Ser 2008-1206		0	.31		07/07/10		2,200,000
	5,480	New York State Environmental Facilities Corporation, Ser 2002 B Custody Receipts Ser 2008-3051X		0	.31		07/07/10		5,480,000
	2,640	Barclays Capital Municipal Trust Receipts, Battery Park City Authority Ser 2009 B Floater-TRs Ser 1B		0	.28		07/07/10		2,640,000
		City of New York,
	1,000	Fiscal 1994 Ser A Subser A-4		0	.13		07/01/10		1,000,000
	2,050	Fiscal 2004 Ser A Subser A-5		0	.19		07/07/10		2,050,000
	3,200	Fiscal 2004 Ser H Subser H-2		0	.17		07/07/10		3,200,000
	3,300	Fiscal 2006 Subser F-3		0	.25		07/07/10		3,300,000
	9,540	Fiscal 2006 Subser I-4		0	.23		07/07/10		9,540,000
	3,100	Fiscal 2008 Ser 2007 Subser D-3		0	.22		07/07/10		3,100,000
	1,900	Fiscal 2008 Subser D-4		0	.25		07/07/10		1,900,000
	2,150	Fiscal 2008 Subser J-4		0	.16		07/01/10		2,150,000
	2,140	JP Morgan Chase & Co., Port Authority of New York & New Jersey Cons Ser 156 PUTTERs Ser 3647		0	.31		07/07/10		2,140,000
		Metropolitan Transportation Authority,
	16,835	Dedicated Tax Ser 2008 B-1 & B-3		0	.28		07/07/10		16,835,000
	3,260	Ser 2002 A PUTTERs Ser 2911Z (AGM Insd)		0	.46		07/07/10		3,260,000
	5,000	Nassau County Interim Finance Authority, Sales Tax Ser 2008 D-2		0	.23		07/07/10		5,000,000
		New York City Housing Development Corporation,
	1,875	James Tower Development 2002 Ser A		0	.19		07/07/10		1,875,000
	2,490	Queens College Residences 2009 Ser A		0	.27		07/07/10		2,490,000
		New York City Industrial Development Agency,
	1,800	FC Hanson Office Associates LLC Ser 2004		0	.30		07/07/10		1,800,000
	6,000	One Bryant Park LLC Ser 2004 A		0	.24		07/07/10		6,000,000
	7,000	United Jewish Appeal Federation Ser 2004 B		0	.22		07/07/10		7,000,000
		New York City Municipal Water Finance Authority,
	3,950	Second General Fiscal 2007 Ser CC-1		0	.14		07/01/10		3,950,000
	1,000	Second General Fiscal 2010 Ser CC		0	.28		07/07/10		1,000,000
		New York City Transitional Finance Authority,
	7,600	Future Tax Fiscal 2001 Ser B		0	.13		07/01/10		7,600,000
	1,800	Future Tax Fiscal 2003 Ser C Subser C2		0	.13		07/01/10		1,800,000
	3,300	Future Tax Fiscal 2003 Ser C Subser C4		0	.20		07/07/10		3,300,000
		New York City Trust for Cultural Resources,
	5,000	American Museum of Natural History Ser 2008 B2		0	.25		07/07/10		5,000,000
	4,100	American Museum of Natural History Ser 2008 B3		0	.25		07/07/10		4,100,000

See Notes to Financial Statements

9

Morgan Stanley New York Municipal Money Market Trust

Portfolio of Investments - June 30, 2010 (unaudited) continued

PRINCIPAL
AMOUNT IN			COUPON				DEMAND
THOUSANDS			RATE (a)				DATE (b)	VALUE
$	1,000	New York Liberty Development Corporation, World Trade Center Ser 2009 A		0	.50	%	01/18/11	$	1,000,000
		New York Local Government Assistance Corporation,
	6,450	Ser 1995 D		0	.20		07/07/10		6,450,000
	6,755	Ser 1995 E		0	.23		07/07/10		6,755,000
	3,800	Ser 1995 F		0	.22		07/07/10		3,800,000
		New York State Dormitory Authority,
	5,200	Columbia University Ser 2003 B		0	.24		07/07/10		5,200,000
	4,500	New York Law School Ser 2009		0	.25		07/07/10		4,500,000
	8,220	Pratt Institute Ser 2009 B		0	.31		07/07/10		8,220,000
	7,300	Rockefeller University Ser 2009 B		0	.26		07/07/10		7,300,000
	3,970	Wagner College Ser 2009		0	.24		07/07/10		3,970,000
	3,495	New York State Environmental Facilities Corporation, Clean Water & Drinking Ser 2008 B PUTTERs Ser 2900		0	.31		07/07/10		3,495,000
		New York State Housing Finance Agency,
	2,500	Related-Taconic West 17th Street Ser 2009 A		0	.20		07/07/10		2,500,000
	1,850	Service Contract 2003 Ser L		0	.20		07/07/10		1,850,000
		New York State Urban Development Corporation,
	7,420	Personal Income Tax Ser B PUTTERs Ser 2887		0	.31		07/07/10		7,420,000
	4,425	Service Contract Ser 2008-A-1		0	.26		07/07/10		4,425,000
		Triborough Bridge & Tunnel Authority,
	3,830	Ser 2001 A Municipal Securities Trust Receipts Ser 2008 SGC-54 Class A		0	.31		07/07/10		3,830,000
	3,700	Sub Ser 2001 B		0	.17		07/07/10		3,700,000
		Total New York Tax-Exempt Short-Term Variable Rate Municipal Obligations (Cost $186,875,000)							186,875,000

							YIELD TO
							MATURITY
		COUPON				MATURITY	ON DATE OF
		RATE				DATE	PURCHASE
	New York Tax-Exempt Commercial Paper (6.1%)
	Long Island Power Authority,
4,000	Electric System Ser 2008 CP-3		0	.28	%	07/13/10		0.28	%	4,000,000
4,000	Electric System Ser 2008 CP-3		0	.30		08/18/10		0.30		4,000,000
	New York State Power Authority,
2,500	Ser 2		0	.32		08/11/10		0.32		2,500,000
2,500	Ser 2		0	.30		08/16/10		0.30		2,500,000
	Total New York Tax-Exempt Commercial Paper (Cost $13,000,000)									13,000,000
	New York Tax-Exempt Short-Term Municipal Notes and Bonds (5.4%)
4,000	Metropolitan Transportation Authority, Ser 2010 RANs, dtd 03/31/10		2	.00		12/31/10		0.38		4,032,235

See Notes to Financial Statements

10

Morgan Stanley New York Municipal Money Market Trust

Portfolio of Investments - June 30, 2010 (unaudited) continued

								YIELD TO
PRINCIPAL								MATURITY
AMOUNT IN			COUPON				MATURITY	ON DATE OF
THOUSANDS			RATE				DATE	PURCHASE			VALUE
$	4,900	Saugerties Central School District, Ser 2010 RANs, dtd 06/23/10		1	.25	%	10/29/10		0.98	%	$	4,904,318
	1,378	South Glens Falls Central School District, Ser 2009 BANs, dtd 09/03/09		1	.75		08/04/10		1.21			1,378,819
	1,055	Van Hornesville-Owen D Young Central School District, Ser 2009 BANs, dtd 12/10/09		1	.75		07/09/10		1.05			1,055,161
		Total New York Tax-Exempt Short-Term Municipal Notes and Bonds (Cost $11,370,533)										11,370,533
		Total Investments (Cost $211,245,533) (c)							100.0	%		211,245,533
		Liabilities in Excess of Other Assets							0.0			(4,060	)
		Net Assets							100.0	%	$	211,241,473

BANs	Bond Anticipation Notes.
PUTTERs	Puttable Tax-Exempt Receipts.
RANs	Revenue Anticipation Notes.
(a)	Rate shown is the rate in effect at June 30, 2010.
(b)	Date on which the principal amount can be recovered through demand.
(c)	Cost is the same for federal income tax purposes.
Bond Insurance:
AGM	Assured Guaranty Municipal Corporation.

See Notes to Financial Statements

11

Morgan Stanley New York Municipal Money Market Trust

Financial Statements

Statement of Assets and Liabilities

June 30, 2010 (unaudited)

Assets:
Investments in securities, at value (cost $211,245,533)	$	211,245,533
Cash		54,827
Receivable for:
Interest		114,844
Shares of beneficial interest sold		34,695
Prepaid expenses and other assets		18,342
Total Assets		211,468,241
Liabilities:
Payable for:
Shares of beneficial interest redeemed		49,287
Investment advisory fee		38,933
Administration fee		9,518
Transfer agent fee		4,317
Accrued expenses and other payables		124,713
Total Liabilities		226,768
Net Assets	$	211,241,473
Composition of Net Assets:
Paid-in-capital	$	211,284,983
Dividends in excess of net investment income		(42,777	)
Accumulated net realized loss		(733	)
Net Assets	$	211,241,473
Class R Shares
Net Assets		$36,033,811
Shares Outstanding (unlimited shares authorized, $.01 par value)		36,019,725
Net Asset Value Per Share		$1.00
Class S shares:
Net Assets		$175,207,662
Shares Outstanding (unlimited shares authorized, $.01 par value)		175,157,519
Net Asset Value Per Share		$1.00

See Notes to Financial Statements

12

Morgan Stanley New York Municipal Money Market Trust

Financial Statements continued

Statement of Operations

For the six months ended June 30, 2010 (unaudited)

Net Investment Income:
Income
Interest	$	348,398
Dividends from affiliate		2
Total Income		348,400
Expenses
Investment advisory fee		468,400
Shareholder service fee		104,089
Administration fee		52,044
Professional fees		39,448
Shareholder reports and notices		16,538
Trustees’ fees and expenses		12,786
Transfer agent fees and expenses		7,892
Custodian fees		4,387
Registration fees		2,870
Other		11,867
Total Expenses		720,321
Less: amounts waived/reimbursed		(381,321	)
Less: rebate from Morgan Stanley affiliated cash sweep (Note 5)		(41	)
Net Expenses		338,959
Net Investment Income		9,441
Net Realized Loss		(733	)
Net Increase	$	8,708

See Notes to Financial Statements

13

Morgan Stanley New York Municipal Money Market Trust

Financial Statements continued

Statements of Changes in Net Assets

	FOR THE SIX			FOR THE YEAR
	MONTHS ENDED			ENDED
	JUNE 30, 2010			DECEMBER 31, 2009
	(unaudited)
Increase (Decrease) in Net Assets:
Operations:
Net investment income	$	9,441		$	148,207
Net realized gain (loss)		(733	)		47,983
Net Increase		8,708			196,190
Dividends to Shareholders from Net Investment Income:
Class R shares		(1,896	)		(22,335	)
Class S shares		(8,510	)		(126,833	)
Total Dividends		(10,406	)		(149,168	)
Net decrease from transactions in shares of beneficial interest		(4,394,175	)		(341,437,411	)
Net Decrease		(4,395,873	)		(341,390,389	)
Net Assets:
Beginning of period		215,637,346			557,027,735
End of Period (Including dividends in excess of net investment income of $42,777 and $41,812, respectively)	$	211,241,473		$	215,637,346

See Notes to Financial Statements

14

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial Statements - June 30, 2010 (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 & Co. Incorporated, an affiliate of Morgan Stanley Investment Advisors Inc. (the “Investment 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 market value, in accordance with Rule 2a-7 under the Act.

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. Federal Income Tax Policy — It is the Fund’s policy to comply with the requirements of Subchapter M of the Internal Revenue Code applicable to regulated investment companies and to distribute substantially all of its taxable and non-taxable income to its shareholders. Therefore, no federal income tax provision is required. The Fund files tax returns with the U.S. Internal Revenue Service, New York State and New York City. The Fund recognizes the tax effects of a tax position taken or expected to be taken in a tax return only if it is more likely than not to be sustained based solely on its technical merits as of the reporting date. The more-likely-than-not threshold must continue to be met in each reporting period to support continued recognition of the benefit. The difference between the tax benefit recognized in the financial statements for a tax position taken and the tax benefit claimed in the income tax return is referred to as an unrecognized tax benefit. There are no unrecognized tax benefits in the accompanying financial statements. If applicable, the Fund recognizes interest accrued related to unrecognized tax benefits in interest expense and penalties in

15

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial Statements - June 30, 2010 (unaudited) continued

other expenses in the Statement of Operations. Each of the tax years filed in the four-year period ended December 31, 2009 remains subject to examination by taxing authorities.

E. Dividends and Distributions to Shareholders — The Fund records dividends and distributions to shareholders as of the close of each business day.

F. 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.

G. Subsequent Events — The Fund considers events or transactions that occur after the date of the Statement of Assets and Liabilities but before the financial statements are issued to provide additional evidence relative to certain estimates or to identify matters that require additional disclosure. Subsequent events have been evaluated through the date of issuance of these financial statements.

H. 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.

2. Fair Valuation Measurements

Financial Accounting Standards Board Accounting Standards Codification (ASC) 820, Fair Value Measurements and Disclosures (ASC 820) (formerly known as FAS 157), defines fair value as the price 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 pricing 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 pricing 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.)

16

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial Statements - June 30, 2010 (unaudited) continued

•  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 as of June 30, 2010 in valuing the Fund’s investments carried at fair value:

			FAIR VALUE MEASUREMENTS AT JUNE 30, 2010 USING
			UNADJUSTED		OTHER
			QUOTED PRICES IN		SIGNIFICANT		SIGNIFICANT
			ACTIVE MARKET FOR		OBSERVABLE		UNOBSERVABLE
			IDENTICAL INVESTMENTS		INPUTS		INPUTS
INVESTMENT TYPE	TOTAL		(LEVEL 1)		(LEVEL 2)		(LEVEL 3)
New York Tax-Exempt Short-Term Variable Rate Municipal Obligations	$	186,875,000		—	$	186,875,000		—
New York Tax-Exempt Commercial Paper		13,000,000		—		13,000,000		—
New York Tax-Exempt Short-Term Municipal Notes and Bonds		11,370,533		—		11,370,533		—
Total	$	211,245,533		—	$	211,245,533		—

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, 2010, the Fund did not have any investments transfer between valuation levels.

3. Investment Advisory/Administration Agreements

Pursuant to an Investment Advisory Agreement with the Investment Adviser, the Fund pays the Investment 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.

17

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial Statements - June 30, 2010 (unaudited) continued

Pursuant to an Administration Agreement with Morgan Stanley Services Company Inc. (the “Administrator”), an affiliate of the Investment 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 an 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 Investment Adviser has voluntarily agreed to cap the Fund’s operating expenses by assuming the Fund’s “other expenses” and/or waiving the Fund’s advisory fees, and the Administrator has agreed to waive the Fund’s administrative fees, to the extent that such operating expenses exceed 0.60% of the average daily net assets of the Fund on an annualized basis.

4. Shareholder Services Plan

Pursuant to a Shareholder Service Plan (the “Plan”), the Fund may pay Morgan Stanley Distributors 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.

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, 2010, the distribution fee was accrued at the annual rate of 0.10%.

The Distributor, Investment Adviser and Administrator have voluntarily agreed to waive/reimburse all or a portion of the Fund’s shareholder servicing fee, investment 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, 2010, the Distributor waived $104,089 and the Investment Adviser waived $277,232. The fee waiver and/or expense reimbursements are expected to continue until such time that the Board of Trustees acts to discontinue such waivers and/or reimbursements when it deems such action is appropriate.

5. Security Transactions and Transactions with Affiliates

The Fund invests in Morgan Stanley Institutional Liquidity Funds – Government Portfolio – Institutional Class, an open-end management investment company managed by an affiliate of the Investment Adviser. Investment advisory fees paid by the Fund are reduced by an amount equal to the advisory and administrative service fees paid by Morgan Stanley Institutional Liquidity Funds – Government Portfolio – Institutional Class with respect to assets invested by the Fund in Morgan Stanley Institutional Liquidity Funds – Government Portfolio – Institutional Class. For the six months ended June 30, 2010, advisory fees paid were reduced by $41 relating to the Fund’s investment in Morgan Stanley Institutional Liquidity Funds – Government Portfolio –

18

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial Statements - June 30, 2010 (unaudited) continued

Institutional Class. Income distributions earned by the Fund are recorded as “dividends from affiliate” in the Statement of Operations and totaled $2 for the six months ended June 30, 2010. During the six months ended June 30, 2010, the cost of purchases and sales of investments in Morgan Stanley Institutional Liquidity Funds – Government Portfolio – Institutional Class aggregated $5,300,000 and $5,300,000, respectively.

The cost of purchases and proceeds from sales/maturities of portfolio securities for the six months ended June 30, 2010 aggregated $305,543,884 and $309,444,556, respectively. Included in the aforementioned transactions are purchases and sales of $8,220,000 and $2,820,000, respectively, with other Morgan Stanley Funds.

Morgan Stanley Services Company Inc., an affiliate of the Investment Adviser and Distributor, is the Fund’s transfer agent.

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, 2010, included in “trustees’ fees and expenses” in the Statement of Operations amounted to $9,767. At June 30, 2010, the Fund had an accrued pension liability of $63,761, which is included in “accrued expenses and other payables” in the Statement of Assets and Liabilities.

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 he or she receives 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.

19

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial Statements - June 30, 2010 (unaudited) continued

6. Shares of Beneficial Interest

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

	FOR THE SIX			FOR THE YEAR
	MONTHS ENDED			ENDED
	JUNE 30, 2010			DECEMBER 31, 2009
	(unaudited)
CLASS R SHARES
Shares sold		14,834,012			31,166,431
Shares issued in reinvestment of dividends		1,896			22,335
Shares redeemed		(17,027,546	)		(63,687,322	)
Net decrease – Class R		(2,191,638	)		(32,498,556	)
CLASS S SHARES
Shares sold		325,078,280			819,364,303
Shares issued in reinvestment of dividends		8,510			126,833
Shares redeemed		(327,289,327	)		(1,128,429,991	)
Net decrease – Class S		(2,202,537	)		(308,938,855	)
Net decrease in Fund		(4,394,175	)		(341,437,411	)

7. Federal Income Tax Status

The amount of dividends and distributions from net investment income and net realized capital gains are determined in accordance with federal income tax regulations which may differ from GAAP. These “book/tax” differences are either considered temporary or permanent in nature. To the extent these differences are permanent in nature, such amounts are reclassified within the capital accounts based on their federal tax-basis treatment; temporary differences do not require reclassification. Dividends and distributions which exceed net investment income and net realized capital gains for tax purposes are reported as distributions of paid-in-capital.

As of December 31, 2009, the Fund had temporary book/tax differences primarily attributable to nondeductible expenses.

8. New Accounting Pronouncement

On January 21, 2010, the Financial Accounting Standards Board issued Accounting Standards Update (“ASU”) 2010-06. The ASU amends Accounting Standards Codification 820 to add new requirements for disclosures about transfers into and out of Levels 1 and 2 and separate disclosures about purchases, sales, issuances, and settlements relating to Level 3 measurements. It also clarifies existing fair value disclosures about the level of disaggregation and about inputs and valuation techniques in Level 2 and Level 3 fair value measurements. The application of ASU 2010-06 is required for fiscal years and interim periods beginning after December 15, 2009, except for disclosures about purchases, sales, issuances, and settlements relating to Level 3 measurements, which are required for fiscal years beginning after December 15, 2010 and for interim periods within those fiscal years.

20

Morgan Stanley New York Municipal Money Market Trust

Financial Highlights

	FOR THE SIX
	MONTHS ENDED			FOR THE YEAR ENDED DECEMBER 31,
	JUNE 30, 2010			2009			2008			2007			2006			2005
	(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)		0.015			0.031			0.028			0.018
Less dividends from net investment income		(0.000	)(1)		(0.000	)(1)		(0.015	)(2)		(0.031	)		(0.028	)		(0.018	)
Net asset value, end of period		$1.00			$1.00			$1.00			$1.00			$1.00			$1.00
Total Return		0.00	%(7)		0.04	%		1.54	%		3.13	%		2.86	%		1.84		%
Ratios to Average Net Assets:(3)
Total expenses		0.33	%(4)(8)		0.52	%(4)(5)		0.62	%(4)(5)		0.61	%		0.60	%		0.61		%
Net investment income		0.00	%(4)(8)		0.05	%(4)(5)		1.43	%(4)(5)		2.99	%		2.84	%		1.81		%
Rebate from Morgan Stanley affiliate		0.00	%(6)(8)		0.00	%(6)		0.02	%		—			—			—
Supplemental Data:
Net assets, end of period, in thousands		$36,034			$38,226			$70,716			$85,548			$93,184			$65,107

(1)	Amount is less than $0.001.
(2)	Includes a long-term capital gain distribution of less than $0.005.
(3)	If the Fund had borne all expenses that were reimbursed or waived by the Distributor, Investment Adviser and Administrator, the annualized expense and net investment income (loss) ratios would have been as follows:

	EXPENSE			NET INVESTMENT
PERIOD ENDED	RATIO			INCOME (LOSS) RATIO
June 30, 2010		0.70	%		(0.37	)%
December 31, 2009		0.74			(0.17	)
December 31, 2008		0.65			1.40
December 31, 2007		0.77			2.83
December 31, 2006		0.89			2.55
December 31, 2005		0.86			1.56

(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 Guarantee Program for Money Markets Funds. This fee had an effect of 0.07% and 0.02% for the year ended 2009 and 2008, respectively.
(6)	Amount is less than 0.005%.
(7)	Not annualized.
(8)	Annualized.

See Notes to Financial Statements

21

Morgan Stanley New York Municipal Money Market Trust

Financial Highlights continued

				FOR THE YEAR						FOR THE PERIOD
	FOR THE SIX			ENDED						SEPTEMBER 17, 2007*
	MONTHS ENDED			DECEMBER 31,						THROUGH
	JUNE 30, 2010			2009			2008			DECEMBER 31, 2007
	(unaudited)
Class S Shares
Selected Per Share Data:
Net asset value, beginning of period		$1.00			$1.00			$1.00			$1.00
Net income from investment operations		0.000	(1)		0.000	(1)		0.015			0.008
Less dividends from net investment income		(0.000	)(1)		(0.000	)(1)		(0.015	)(2)		(0.008	)
Net asset value, end of period		$1.00			$1.00			$1.00			$1.00
Total Return		0.00	%(7)		0.04	%		1.54	%		0.83		%(7)
Ratios to Average Net Assets:(3)
Total expenses		0.33	%(4)(8)		0.52	%(4)(5)		0.62	%(4)(5)		0.61		%(8)
Net investment income		0.00	%(4)(8)		0.05	%(4)(5)		1.43	%(4)(5)		2.99		%(8)
Rebate from Morgan Stanley affiliate		0.00	%(6)(8)		0.00	%(6)		0.02	%		—
Supplemental Data:
Net assets, end of period, in thousands		$175,208			$177,412			$486,311			$132,583

*	Commencement of operations.
(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 expenses that were waived by the Distributor, Investment Adviser and Administrator, the annualized expense and net investment income (loss) ratios would have been as follows:

	EXPENSE			NET INVESTMENT
PERIOD ENDED	RATIO			INCOME (LOSS) RATIO
June 30, 2010		0.70	%		(0.37	)%
December 31, 2009		0.74			(0.17	)
December 31, 2008		0.65			1.40
December 31, 2007		0.77			2.83

(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 Guarantee Program for Money Markets Funds. This fee had an effect of 0.07% and 0.02% for the year ended 2009 and 2008, respectively.
(6)	Amount is less than 0.005%.
(7)	Not annualized.
(8)	Annualized.

See Notes to Financial Statements

22

Morgan Stanley New York Municipal Money Market Trust

An Important Notice Concerning Our U.S. Privacy Policy (unaudited)

We are required by federal law to provide you with a copy of our privacy policy (“Policy”) annually.

This Policy applies to current and former individual clients of Morgan Stanley Distributors Inc., as well as current and former individual investors in Morgan Stanley mutual funds and related companies.

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, 529 Educational Savings Accounts, accounts subject to the Uniform Gifts to Minors Act, or similar accounts. We may amend this Policy at any time, and will inform you of any changes to this 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 safeguarding such information. We strive to maintain the privacy of such information while we help you achieve your financial objectives. This Policy describes what non-public personal information we collect about you, how we collect it, when we may share it with others, and how others may use it. It discusses the steps you may take to limit our sharing of information about you with affiliated Morgan Stanley companies (“affiliated companies”). It also discloses how you may limit our affiliates’ use of shared information for marketing purposes. Throughout this Policy, we refer to the non-public information that personally identifies you or your accounts as “personal information.”

1.  What Personal Information Do We Collect About You?

To better serve you and manage our business, it is important that we collect and maintain accurate information about you. We obtain this information from applications and other forms you submit to us, from your dealings with us, from consumer reporting agencies, from our websites and from third parties and other sources.

For example:

•  We collect information such as your name, address, e-mail address, telephone/fax numbers, assets, income and investment objectives through application 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.

23

Morgan Stanley New York Municipal Money Market Trust

An Important Notice Concerning Our U.S. Privacy Policy (unaudited) continued

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

•  If you interact with us through our public and private Web sites, we may collect information that you provide directly through online communications (such as an e-mail address). We may also collect information about your Internet service provider, your domain name, your computer’s operating system and Web browser, your use of our Web sites and your product and service preferences, through the use of “cookies.” “Cookies” recognize your computer each time you return to one of our sites, and help to improve our sites’ content and personalize your experience on our sites by, for example, suggesting offerings that may interest you. Please consult the Terms of Use of these sites for more details on our use of cookies.

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

To provide you with the products and services you request, to better serve you, to manage our business and as otherwise required or permitted by law, we may disclose personal information we collect about you to other affiliated companies and to non-affiliated third parties.

A. Information We Disclose to Our Affiliated Companies.  In order to manage your account(s) effectively, including servicing and processing your transactions, 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, we may disclose personal information about you to other affiliated companies. 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 do not disclose personal information that we collect about you to non-affiliated third parties except to enable them to provide marketing services on our behalf, to perform joint marketing agreements with other financial institutions, and as otherwise required or permitted by law. For example, some instances where we may disclose information about you to third parties include: for servicing and processing transactions, to offer our own products and services, to protect against fraud, for institutional risk control, to respond to judicial process or to perform services on our behalf. When we share personal information with a non-affiliated 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 required by law.

3.  How Do We Protect the Security and Confidentiality of Personal Information We Collect About You?

We maintain physical, electronic and procedural security measures to help safeguard the personal information we collect about you. We have internal policies governing the proper handling of client information. Third parties that provide support or marketing services on our behalf may also receive personal

24

Morgan Stanley New York Municipal Money Market Trust

An Important Notice Concerning Our U.S. Privacy Policy (unaudited) continued

information about you, and we require them to adhere to confidentiality standards with respect to such information.

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

We respect your privacy and offer you choices as to whether we share with our affiliated companies personal information that was collected to determine your eligibility for products and services such as credit reports and other information that you have provided to us or that we may obtain from third parties (“eligibility information”). Please note that, even if you direct us not to share certain eligibility information with our affiliated companies, we may still share your personal information, including eligibility information, with those companies under circumstances that are permitted under applicable law, such as to process transactions or to service your account. We may also share certain other types of personal information with affiliated companies – such as your name, address, telephone number, e-mail address and account number(s), and information about your transactions and experiences with us.

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

You may limit our affiliated companies from using certain personal information about you that we may share with them for marketing their products or services to you. This information includes our transactions and other experiences with you such as your assets and account history. Please note that, even if you choose to limit our affiliated companies from using certain personal information about you that we may share with them for marketing their products and services to you, we may still share such personal information about you with them, including our transactions and experiences with you, for other purposes as permitted under applicable law.

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

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

•  Calling us at (800) 869-6397
Monday-Friday between 8a.m. and 8p.m. (EST)

•  Writing to us at the following address:
Morgan Stanley Privacy Department
Harborside Financial Center, Plaza Two, 3rd Floor
Jersey City, NJ 07311

25

Morgan Stanley New York Municipal Money Market Trust

An Important Notice Concerning Our U.S. Privacy Policy (unaudited) continued

If you choose to write to us, your written request should include: your name, address, telephone number and account number(s) to which the opt-out applies and 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 allow approximately 30 days from our receipt of your opt-out for your instructions to become effective.

Please understand that if you opt-out, you and any joint account holders may not receive certain Morgan Stanley or our affiliated companies’ products and services that could help you manage your financial resources and achieve your investment objectives.

If you have more than one account with us or our affiliates, you may receive multiple privacy policies from us, and would need to follow the directions stated in each particular policy for each account you have with us.

Special Notice to Residents of Vermont

This 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 affiliated companies and non-affiliated third parties other than in certain limited circumstances. Except as permitted by law, we will not share personal information we collect about you with non-affiliated third parties or other affiliated companies unless you provide us with your written consent to share such information (“opt-in”).

If you wish to receive offers for investment products and services offered by or through other affiliated companies, please notify us in writing at the following address:

Morgan Stanley Privacy Department
Harborside Financial Center, Plaza Two, 3rd Floor
Jersey City, NJ 07311

Your authorization should include: your name, address, telephone number and account number(s) to which the opt-in applies and should not be sent with any other correspondence. In order to process your authorization, we require that the authorization be provided by you directly and not through a third-party.

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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

Randy Takian

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

Morgan Stanley Services Company, Inc.

Harborside Financial Center, Plaza Two

Jersey City, New Jersey 07311

Independent Registered Public Accounting Firm

Deloitte & Touche LLP

Two World Financial Center

New York, New York 10281

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

Investment Adviser

Morgan Stanley Investment Advisors 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. Read the Prospectus carefully before investing.

Morgan Stanley Distributors Inc., member FINRA.

(c)  2010 Morgan Stanley

INVESTMENT MANAGEMENT

Morgan Stanley

New York Municipal Money Market Trust

Semiannual
Report

June 30, 2010

DWNSAN

IU10-03002P-Y06/10

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 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/ Randy Takian

Randy Takian

Principal Executive Officer

August 17, 2010

     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/ Randy Takian

Randy Takian

Principal Executive Officer

August 17, 2010

/s/ Francis Smith

Francis Smith

Principal Financial Officer

August 17, 2010

3