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)

John H. Gernon

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,

Date of reporting period: June 30, 2020

Item 1 - Report to Shareholders

INVESTMENT MANAGEMENT

Morgan Stanley New York Municipal
Money Market Trust

Semi-Annual Report

June 30, 2020

Beginning on January 1, 2021, as permitted by regulations adopted by the Securities and Exchange Commission ("SEC"), paper copies of the Fund's Annual and Semi-Annual Reports to Shareholders ("Shareholder Reports") will no longer be sent by mail, unless you specifically request paper copies of the Shareholder Reports from the Fund or from your financial intermediary, such as a broker-dealer or a bank. Instead, the Shareholder Reports will be made available on the Fund's website, https://www.morganstanley.com/im/moneymarketfundsshareholderreports and you will be notified by mail each time a Shareholder Report is posted and provided with a website link to access the Shareholder Report. If you already elected to receive Shareholder Reports electronically, you will not be affected by this change and you need not take any action. You may elect to receive Shareholder Reports and other communications from the Fund electronically anytime by contacting your financial intermediary or, if you are a direct investor, please follow the instructions on the envelope.

Beginning on January 1, 2019, you may elect to receive all future Shareholder Reports in paper free of charge. If you invest through a financial intermediary, you can contact your financial intermediary to request that you continue to receive paper copies of your Shareholder Reports. If you invest directly with the Fund, please follow the instructions on the envelope to let the Fund know you wish to continue receiving paper copies of your Shareholder Reports. Your election to receive Shareholder Reports in paper will apply to all funds held in your account if you invest through your financial intermediary or all funds held with the fund complex if you invest directly with a fund.

Morgan Stanley New York Municipal Money Market Trust

Table of Contents

Welcome Shareholder		3
Fund Report		4
Expense Example		8
Portfolio of Investments		9
Statement of Assets and Liabilities		11
Statement of Operations		12
Statements of Changes in Net Assets		13
Notes to Financial Statements		14
Financial Highlights		21
Investment Advisory Agreement Approval		23
Privacy Notice		26
Trustee and Officer Information	Back Cover

Welcome Shareholder,

We are pleased to provide this Semi-Annual Report, in which you will learn how your investment in Morgan Stanley New York Municipal Money Market Trust (the "Fund") 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. You could lose money by investing in the Fund. Although the Fund seeks to preserve the value of your investment at $1.00 per share, it cannot guarantee it will do so. The Fund may impose a fee upon the sale of your shares or may temporarily suspend your ability to sell shares if the Fund's liquidity falls below required minimums because of market conditions or other factors. An investment in the Fund is not insured or guaranteed by the Federal Deposit Insurance Corporation or any other government agency. The Fund's sponsor has no legal obligation to provide financial support to the Fund and you should not expect that the sponsor will provide financial support to the Fund at any time.

Fund Report (unaudited)

For the six months ended June 30, 2020

Market Conditions

Municipal bonds experienced significant volatility in the first half of 2020, triggered by the global pandemic. The increase in tax-exempt money market fund yields in March 2020 was largely a supply and demand situation related to redemption activity across the money market fund industry. Daily and weekly variable rate demand obligations (VRDOs) saw rates spike to levels over 8 percent.⁽ⁱ⁾ As fund flows stabilized across money markets and supply in tax-exempt securities became limited, yields dropped. At the same time, the Federal Reserve (Fed) and other central banks around the world injected liquidity into the short-term markets. To combat the economic slowdown from the prolonged shutdown, the Fed announced that to support the economy it would extend asset purchases (known as quantitative easing) to an unlimited amount and also include other assets such as corporate and municipal bonds. In addition, the Fed created the Money Market Liquidity Facility (MMLF) to support prime and tax-exempt money markets. Importantly, the concerns created in the overall money market industry were largely unrelated to tax-exempt/municipal securities; this was a liquidity crisis.

On April 9, 2020, the Fed announced the creation of the Municipal Liquidity Facility (MLF) to help state and local governments better manage cash flow pressures in order to continue to serve households and businesses in their communities. With the creation of the MLF, the broader municipal market stabilized and began to normalize through May 2020. Municipals continued to see a rebound in June 2020, amid the domestic economy reopening. Supply picked up more than

expected in June, with issuance of $48.7 billion.⁽ⁱⁱ⁾ Taxable municipal issuance was a major contributor to this acceleration. The increased supply was met with firm demand. Municipal bond mutual funds, many of which were already holding elevated levels of cash, experienced $10.8 billion of inflows in June 2020 according to Lipper.

State and local governments will face significant headwinds as they finalize their 2021 and 2022 budgets. Some states with June 30 budget deadlines remain without budgets as they struggle with depressed tax collections and ongoing budgetary challenges due to the coronavirus pandemic, as well as a potential second wave of infections that is forcing many to slow reopening. Many state and local municipalities may be forced to cut services and public sector jobs to balance their budgets, a move that could further negatively impact tax collections.

The Bureau of Labor Statistics (BLS) data confirms the New York State economy is undergoing a dramatic contraction as a result of the reduction in economic activity due to the COVID-19 pandemic. The unemployment rate increased from 4.1 percent in March 2020 to 15.1 percent in April 2020 as the state reported a 1.7 million decline in jobs during the month. The majority of employment loss occurred in leisure and hospitality (577,700). As the state's economy has begun a gradual phased reopening, BLS data for May 2020 showed the unemployment rate declining to 14.2 percent as the economy added 137,300 jobs.

(i) Source: Bloomberg L.P. Data as of March 2020.

(ii) Source: The Bond Buyer. Data as of June 2020.

In addition, certain leading economic indicators were beginning to show signs that the economic slowdown in New York may have bottomed out. The Empire State Manufacturing Survey, which measures how factories in New York state view the state of their business, showed that general business conditions improved more than expected in June 2020, following record lows in April and May.

On March 22, 2020, "New York State on PAUSE" went into effect, requiring all non-essential businesses to close. The restrictive measures taken to contain the spread of COVID-19 have resulted in abrupt economic disruption. Actions taken by the federal government, in the form of Federal Reserve policy and legislation, have stabilized financial markets and provided assistance to businesses, individuals and governments. The state's enacted budget for the fiscal year that began April 1, 2020 implemented a 7.1 percent decrease ($7.3 billion) in expenditures, the largest spending reduction since the Great Depression.⁽ⁱⁱⁱ⁾ Additional spending reductions are authorized if taxes and other receipts are materially below estimates.

Performance Analysis

As of June 30, 2020, Morgan Stanley New York Municipal Money Market Trust had net assets of approximately $6.7 million and an average portfolio maturity of 5 days. For the six-month period ended June 30, 2020, the Fund's Class R and Class S shares provided a total return of 0.36 percent. For the seven-day period ended

June 30, 2020, each of the Fund's Class R and Class S shares provided an effective annualized yield of 0.01 percent (subsidized) and -3.79 percent (non-subsidized) and a current yield of 0.01 percent (subsidized) and -3.87 percent (non-subsidized), while the 30-day moving average yield for June was 0.01 percent (subsidized) and -6.81 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. Past performance is no guarantee of future results.

Protecting the safety and liquidity of the portfolio's assets remained our first priority. In the recent turbulent markets, our emphasis has been on managing liquidity and exposure to sectors and issuers that may come under stress as a result of a prolonged economic slowdown caused by the global pandemic. We continue to invest in tax-exempt securities, including VRDOs, 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.

During this period of market upheaval, we continue to diligently access any new developments that may impact the portfolio. We will also continue to closely monitor the implications of the slowing economy on municipal government balance sheets.

(iii) Source: New York Fiscal Year 2021 Enacted Budget Financial Plan, available at https://www.budget.ny.gov/pubs/archive/fy21/enac/fy21-enacted-fp.pdf

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 06/30/20
Weekly Variable Rate Bonds	59.0	%
Daily Variable Rate Bonds	41.0
MATURITY SCHEDULE as of 06/30/20
1 - 30 Days	100.0	%

Subject to change daily. Provided for informational purposes only and should not be deemed as a recommendation to buy or sell the types of securities mentioned above. All percentages for portfolio composition and maturity schedule are stated 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.

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 Fund's "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 Semi-Annual and Annual Reports within 60 days of the end of the fund's second and fourth fiscal quarters. The Semi-Annual 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 Semi-Annual and Annual Reports to fund shareholders and makes these reports available on its public website, www.morganstanley.com/im/moneymarketfundsshareholderreports. Each Morgan Stanley non-money market fund also files a complete schedule of portfolio holdings with the SEC for the fund's first and third fiscal quarters as an attachment to Form N-PORT 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 website. However, the holdings for each money market fund are posted to the Morgan Stanley public website. You may obtain the Form N-PORT filings (as well as the Form N-CSR, N-CSRS and N-MFP filings) by accessing the SEC's website, http://www.sec.gov. 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).

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) 548-7786, 8:00 a.m. to 6:00 p.m., ET. Once our Customer Service Center has received your instructions, we will begin sending individual copies for each account within 30 days.

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 01/01/20 – 06/30/20.

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⁽¹⁾
	01/01/20		06/30/20		01/01/20 – 06/30/20
Class R
Actual (0.36% return)	$	1,000.00	$	1,003.63	$	0.84
Hypothetical (5% annual return before expenses)	$	1,000.00	$	1,023.89	$	0.85
Class S
Actual (0.36% return)	$	1,000.00	$	1,003.62	$	0.84
Hypothetical (5% annual return before expenses)	$	1,000.00	$	1,023.89	$	0.85

(1) Expenses are equal to the Fund's annualized expense ratios of 0.17% and 0.17% for Class R and Class S shares, respectively, multiplied by the average account value over the period and multiplied by 181**/366 (to reflect the one-half year period). If the Fund had borne all of its expenses, the annualized expense ratios would have been 4.78% and 4.78% for Class R and Class S shares, respectively.

** Adjusted to reflect non-business day accruals.

Morgan Stanley New York Municipal Money Market Trust

Portfolio of Investments n June 30, 2020 (unaudited)

PRINCIPAL AMOUNT (000)			COUPON RATE			DEMAND DATE (a)	MATURITY DATE	VALUE
		Weekly Variable Rate Bonds (b)(59.1%)
$	325	Nassau County Interim Finance Authority, NY, Sales Tax Ser 2008 B		0.12	%	07/07/20	11/15/21	$	325,000
		New York City Cultural Resources Trust, NY,
	325	American Museum of Natural History Ser 2008 B3		0.13		07/07/20	04/01/29		325,000
	325	The Pierpont Morgan Library Ser 2004		0.13		07/07/20	02/01/34		325,000
	300	New York City Housing Development Corp., NY, Multi Family Queenswood Apts Ser 2001 A		0.10		07/07/20	04/01/31		300,000
		New York State Dormitory Authority,
	150	City University System Cons 5th Ser 2008 C		0.13		07/07/20	07/01/31		150,000
	325	Columbia University Ser 2009 A		0.07		07/07/20	09/01/39		325,000
	325	Cornell University Ser 2004 B		0.08		07/07/20	07/01/33		325,000
	270	Fordham University Ser 2008 A-2		0.10		07/07/20	07/01/32		270,000
	250	Highland Cmnty Dev Corp Ser 1994 B		0.15		07/07/20	07/01/23		250,000
	150	Mental Health Services Facilities Ser 2003 D-2E		0.13		07/07/20	02/15/31		150,000
	250	Royal Charter Properties Ser 2006 A		0.10		07/07/20	11/15/36		250,000
	300	St John's University Ser 2008 B-2		0.11		07/07/20	07/01/37		300,000
	325	University of Rochester Ser 2006 A-1		0.10		07/07/20	07/01/27		325,000
	325	New York State Urban Development Corp., Service Contract Ser 2008-A-1		0.13		07/07/20	01/01/30		325,000
		Total Weekly Variable Rate Bonds (Cost $3,945,000)							3,945,000

See Notes to Financial Statements
9

Morgan Stanley New York Municipal Money Market Trust

Portfolio of Investments n June 30, 2020 (unaudited) continued

PRINCIPAL AMOUNT (000)			COUPON RATE			DEMAND DATE (a)	MATURITY DATE			VALUE
		Daily Variable Rate Bonds (b)(41.0%)
$	325	Nassau County Industrial Development Agency, NY, Cold Spring Harbor Laboratory Ser 1999		0.12	%	07/01/20	01/01/34			$	325,000
	330	New York City Industrial Development Agency, NY, New York Stock Exchange Ser 2003 B		0.12		07/01/20	05/01/33				330,000
	325	New York City Municipal Water Finance Authority, NY, Second General Fiscal 2012 Ser A-2		0.11		07/01/20	06/15/44				325,000
	330	New York City Transitional Finance Authority, NY, Future Tax Fiscal 2013 Ser A Subser A-6		0.14		07/01/20	08/01/39				330,000
	330	New York City, NY, Fiscal 2012 Subser G-6		0.13		07/01/20	04/01/42				330,000
		New York State Housing Finance Agency,
	100	160 Madison Avenue Ser 2013 A		0.14		07/01/20	11/01/46				100,000
	200	160 Madison Avenue Ser 2014 A		0.14		07/01/20	11/01/46				200,000
	150	New York State Mortgage Agency, Homeowner Mortgage Ser 135 (AMT)		0.16		07/01/20	04/01/37				150,000
	325	Syracuse Industrial Development Agency, NY, Syracuse University Ser 2008 A-2		0.11		07/01/20	12/01/37				325,000
	325	Triborough Bridge & Tunnel Authority, NY, Ser 2002 F		0.09		07/01/20	11/01/32				325,000
		Total Daily Variable Rate Bonds (Cost $2,740,000)									2,740,000
		Total Investments (Cost $6,685,000) (c)						100.1	%		6,685,000
		Liabilities in Excess of Other Assets						(0.1	)		(6,474	)
		Net Assets						100.0	%	$	6,678,526

AMT Alternative Minimum Tax.

(a) Date on which the principal amount can be recovered through demand.

(b) Floating or variable rate securities: The rates disclosed are as of June 30, 2020. For securities based on a published reference rate and spread, the reference rate and spread are indicated in the description in the Portfolio of Investments. Certain variable rate securities may not be based on a published reference rate and spread but are determined by the issuer or agent and are based on current market conditions. These securities do not indicate a reference rate and spread in their description in the Portfolio of Investments.

(c) The aggregate cost for federal income tax purposes approximates the aggregate cost for book purposes.

See Notes to Financial Statements
10

Morgan Stanley New York Municipal Money Market Trust

Financial Statements

Statement of Assets and Liabilities June 30, 2020 (unaudited)

Assets:
Investments in securities, at value (cost $6,685,000)	$	6,685,000
Cash		27,370
Receivable for:
Interest		547
Due from Adviser		20,497
Prepaid expenses and other assets		39,692
Total Assets		6,773,106
Liabilities:
Payable for:
Trustees' fees		41,868
Transfer agent fees		780
Accrued expenses and other payables		51,932
Total Liabilities		94,580
Net Assets	$	6,678,526
Composition of Net Assets:
Paid-in-capital	$	6,729,666
Total Accumulated Loss		(51,140	)
Net Assets	$	6,678,526
Class R Shares:
Net Assets	$	3,127,827
Shares Outstanding (unlimited shares authorized, $0.01 par value)		3,127,823
Net Asset Value Per Share	$	1.00
Class S Shares:
Net Assets	$	3,550,699
Shares Outstanding (unlimited shares authorized, $0.01 par value)		3,550,699
Net Asset Value Per Share	$	1.00

See Notes to Financial Statements
11

Morgan Stanley New York Municipal Money Market Trust

Financial Statements continued

Statement of Operations For the six months ended June 30, 2020 (unaudited)

Net Investment Income:
Interest Income	$	24,395
Expenses
Professional fees		76,270
Registration fees		18,883
Shareholder reports and notices		8,813
Advisory fee (Note 3)		3,939
Transfer agent fees (Note 5)		2,937
Trustees' fees and expenses		2,804
Custodian fees (Note 6)		2,687
Shareholder services fee (Note 4)		2,626
Administration fee (Note 3)		1,313
Other		5,303
Total Expenses		125,575
Less: amounts waived/reimbursed (Note 3 & 4)		(121,011	)
Net Expenses		4,564
Net Investment Income		19,831
Net Increase	$	19,831

See Notes to Financial Statements
12

Morgan Stanley New York Municipal Money Market Trust

Financial Statements continued

Statements of Changes in Net Assets

	FOR THE SIX MONTHS ENDED JUNE 30, 2020			FOR THE YEAR ENDED DECEMBER 31, 2019
	(unaudited)
Increase (Decrease) in Net Assets:
Operations:
Net investment income	$	19,831		$	70,485
Net Increase		19,831			70,485
Dividends to Shareholders from:
Net investment income
Class R shares		(12,673	)		(62,299	)
Class S shares		(7,158	)		(8,186	)
Total Dividends		(19,831	)		(70,485	)
Net increase (decrease) from transactions in shares of beneficial interest		(1,631,616	)		1,807,761
Net Increase (Decrease)		(1,631,616	)		1,807,761
Net Assets:
Beginning of period		8,310,142			6,502,381
End of Period	$	6,678,526		$	8,310,142

See Notes to Financial Statements
13

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial Statements n June 30, 2020 (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 applies investment company accounting and reporting guidance. 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, Class R and Class S Shares. The two classes have the same fees and expenses.

The Securities and Exchange Commission ("SEC") has adopted changes to the rules that govern money market funds. The Fund operates as a "retail money market fund," which allows the Fund to continue to seek a stable net asset value ("NAV"). The Fund will be permitted to impose a liquidity fee on redemptions from the Fund or temporarily restrict redemptions from the Fund for up to 10 business days.

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. The amortized cost of an instrument is determined by valuing it at its original cost and thereafter amortizing any discount or premium from its face value at a constant rate until maturity. Investments in mutual funds are valued at the NAV 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 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. Shareholder services 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. Dividends from net investment income, if any, are declared and paid daily. Net realized capital gains, if any, are distributed at least annually.

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

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial Statements n June 30, 2020 (unaudited) continued

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.

2. Fair Valuation Measurements

Financial Accounting Standards Board ("FASB") Accounting Standards Codification^TM ("ASC") 820, "Fair Value Measurement" ("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.

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial Statements n June 30, 2020 (unaudited) continued

The following is a summary of the inputs used to value the Fund's investments as of June 30, 2020:

INVESTMENT TYPE	LEVEL 1 UNADJUSTED QUOTED PRICES		LEVEL 2 OTHER SIGNIFICANT OBSERVABLE INPUTS		LEVEL 3 SIGNIFICANT UNOBSERVABLE INPUTS		TOTAL
Assets:
Weekly Variable Rate Bonds	$	—	$	3,945,000	$	—	$	3,945,000
Daily Variable Rate Bonds		—		2,740,000		—		2,740,000
Total Assets	$	—	$	6,685,000	$	—	$	6,685,000

Transfers between investment levels may occur as the markets fluctuate and/or the availability of data used in an investment's valuation changes.

3. Advisory/Administration Agreements

Pursuant to an Investment Advisory Agreement with Morgan Stanley Investment Management Inc. (the "Adviser"), the Fund pays the Adviser an advisory fee, accrued daily and paid monthly, by applying the annual rate of 0.15% to the average net assets of the Fund determined as of the close of each business day.

The Adviser also serves as the Administrator to the Fund and provides administrative services pursuant to an Administration Agreement for an annual fee, accrued daily and paid monthly, of 0.05% of the Fund's average 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 Adviser/Administrator has agreed to assume all operating expenses of the Fund and to waive the advisory fee and administration 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. The fee waivers and/or expense reimbursements will continue for at least one year from the date of the Fund's prospectus 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 they deem such action is appropriate.

In addition, the Adviser and Administrator have also agreed to waive all or a portion of the Fund's advisory fee and administration fee, respectively, and/or reimburse expenses, to the extent that total expense exceed total income of the Fund on a daily basis. These fee waivers and/or expense

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial Statements n June 30, 2020 (unaudited) continued

reimbursements will continue for at least one year or until such time as the Fund's Trustees acts to discontinue all or a portion of such waivers and/or reimbursements when it deems such action is appropriate.

The Adviser and Administrator may make additional voluntary fee waivers and/or expense reimbursements. The ratios of expenses to average net assets disclosed in the Fund's Financial Highlights may be lower than the maximum expense cap of 0.60% due to these additional fee waivers and/or expense reimbursements. The Adviser and Administrator may discontinue these voluntary fee waivers and/or expense reimbursements at any time in the future. For the six months ended June 30, 2020, the Adviser waived $3,939 and the Administrator waived $1,313. For the same period, the Adviser reimbursed additional expenses in the amount of $113,133.

4. Shareholder Services Plan

Pursuant to a Shareholder Services Plan (the "Plan"), the Fund may pay Morgan Stanley Distribution, Inc. (the "Distributor"), an affiliate of the Adviser/Administrator, 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 for Class R and Class S shares.

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, 2020, the distribution fee was accrued at the annual rate of 0.10%. Effective October 10, 2018, the Distributor has agreed to waive all of the Fund's shareholder services fee. For the six months ended June 30, 2020, the Distributor waived $2,626. The fee waivers will continue for at least one year from the date of the Fund's prospectus or until such time that the Fund's Trustees act to discontinue all or a portion of such waivers when they deem such action is appropriate.

The Distributor has agreed to waive all or a portion of the Fund's shareholder services fee and/or reimburse expenses, to the extent that total expenses exceed total income of the Fund on a daily basis. This fee waiver and/or expense reimbursement will continue for at least one year from the date of the Fund's prospectus or until such time that the Trustees act to discontinue all or a portion of such waiver and/or expense reimbursement when they deem such action is appropriate. This arrangement had no effect during the most recent reporting period.

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial Statements n June 30, 2020 (unaudited) continued

5. Dividend Disbursing and Transfer Agent

The Fund's dividend disbursing and transfer agent is DST Asset Manager Solutions, Inc. ("DST"). Pursuant to a Transfer Agency Agreement, the Fund pays DST a fee based on the number of classes, accounts and transactions relating to the Fund.

6. Custodian Fees

State Street (the "Custodian") also serves as Custodian for the Fund in accordance with a Custodian Agreement. The Custodian holds cash, securities and other assets of the Fund as required by the Act. Custody fees are payable monthly based on assets held in custody, investment purchases and sales activity and account maintenance fees, plus reimbursement for certain out-of-pocket expenses.

7. Transactions with Affiliates

The Fund is permitted to purchase and sell securities ("cross-trade") from and to other Morgan Stanley funds as well as other funds and client accounts for which the Adviser or an affiliate of the Adviser serves as investment adviser, pursuant to procedures approved by the Trustees in compliance with Rule 17a-7 under the Act (the "Rule"). Each cross-trade is executed at the current market price in compliance with provisions of the Rule. For the six months ended June 30, 2020, the Fund engaged in cross-trade sales of $1,000,000 which resulted in no net realized gains or losses.

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. At June 30, 2020, the Fund had an accrued pension liability of $41,868, which is reflected as "Trustees' fees" 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 NAV of the Fund.

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial Statements n June 30, 2020 (unaudited) continued

8. 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, 2020			FOR THE YEAR ENDED DECEMBER 31, 2019
	(unaudited)
CLASS R SHARES
Shares sold		12,456			5,895
Shares issued in reinvestment of dividends		12,673			62,299
Shares redeemed		(499,359	)		(2,918,518	)
Net decrease — Class R		(474,230	)		(2,850,324	)
CLASS S SHARES
Shares sold		3,498,534			5,000,034
Shares issued in reinvestment of dividends		7,158			8,186
Shares redeemed		(4,663,078	)		(350,135	)
Net increase (decrease) — Class S		(1,157,386	)		4,658,085
Net increase (decrease) in Fund		(1,631,616	)		1,807,761

9. 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.

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 "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. Generally, each of the tax years in the four-year period ended December 31, 2019 remains subject to examination by taxing authorities.

The tax character of distributions paid may differ from the character of distributions shown for GAAP purposes due to short-term capital gains being treated as ordinary income for tax purposes. The tax character of distributions paid during fiscal years 2019 and 2018 was as follows:

2019 DISTRIBUTIONS PAID FROM:				2018 DISTRIBUTIONS PAID FROM:
TAX-EXEMPT INCOME		ORDINARY INCOME		TAX-EXEMPT INCOME		PAID-IN- CAPITAL
$	70,485	$	—	$	70,429	$	27,566

Morgan Stanley New York Municipal Money Market Trust

Notes to Financial Statements n June 30, 2020 (unaudited) continued

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 distribution in excess of current earnings, resulted in the following reclassifications among the components of net assets at December 31, 2019:

TOTAL ACCUMULATED LOSS				PAID-IN CAPITAL
$	1,602			$	(1,602	)

At December 31, 2019, the Fund had no distributable earnings on a tax basis.

10. Other

At June 30, 2020, the Fund had record owners of 10% or greater. Investment activities of these shareholders could have a material impact on the Fund. The aggregate percentage of such owners was 46.8%.

11. Subsequent Events

Certain impacts to public health conditions particular to the coronavirus (COVID-19) outbreak could impact the operations and financial performance of certain of the Fund's investments. The extent of the impact to the financial performance of the Fund's Investments will depend on future developments, including (i) the duration and spread of the outbreak, (ii) the restrictions and advisories, (iii) the effects on the financial markets, and (iv) the effects on the economy overall, all of which are highly uncertain and cannot be predicted. If the financial performance of the Fund's Investments is impacted because of these factors for an extended period, the Fund's investment results may be adversely affected.

The Trustees of the Fund approved a Plan of Liquidation. Pursuant to the Plan of Liquidation, substantially all of the assets of the Fund will be liquidated, known liabilities of the Fund will be satisfied, the remaining proceeds will be distributed to the Fund's shareholders, all of the issued and outstanding shares of the Fund will be redeemed (the "Liquidation"). The Liquidation is expected to occur on or about September 17, 2020, which is subject to shareholder approval. The Fund will suspend the offering of its shares to all investors at the close of business on or about June 30, 2020.

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			FOR THE YEAR ENDED DECEMBER 31,
	MONTHS ENDED
	JUNE 30, 2020			2019			2018			2017			2016⁽¹⁾			2015
	(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		0.004			0.012			0.009			0.002			0.000	⁽²⁾		0.000	⁽²⁾
Less dividends and distributions from net investment income		(0.004	)		(0.012	)		(0.009	)⁽³⁾		(0.002	)		(0.000	)⁽²⁾⁽⁴⁾		(0.000	)⁽²⁾
Net asset value, end of period	$	1.00		$	1.00		$	1.00		$	1.00		$	1.00		$	1.00
Total Return		0.36	%⁽⁸⁾		1.24	%		0.91	%		0.24	%		0.02	%		0.01	%
Ratios to Average Net Assets⁽⁵⁾:
Net expenses		0.17	%⁽⁹⁾		0.20	%		0.54	%		0.60	%		0.24	%⁽⁶⁾		0.03	%⁽⁶⁾
Net investment income		0.76	%⁽⁹⁾		1.21	%		0.83	%		0.22	%		0.01	%⁽⁶⁾		0.01	%⁽⁶⁾
Rebate from Morgan Stanley affiliate		N/A			N/A			N/A			N/A			0.00	%⁽⁷⁾		0.00	%⁽⁷⁾
Supplemental Data:
Net assets, end of period, in millions	$	3		$	3		$	6		$	10		$	23		$	345

(1) Reflects prior period custodian out-of-pocket expenses that were reimbursed in September 2016. The amount of the reimbursement was immaterial on a per share basis and did not impact the total return of Class R shares. The annualized expense and net investment income ratios would be unchanged as the reimbursement of custodian fees was offset against expense waivers/reimbursements with no impact to net expenses or net investment income.

(2) Amount is less than $0.001.

(3) Includes paid-in-capital distribution of $0.003.

(4) Includes capital gain and paid-in-capital distributions of less than $0.001.

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

PERIOD ENDED	EXPENSE RATIO			NET INVESTMENT LOSS RATIO
June 30, 2020		4.78	%		(3.85	)%
December 31, 2019		4.05			(2.64	)
December 31, 2018		2.03			(0.66	)
December 31, 2017		1.79			(0.97	)
December 31, 2016		0.59			(0.34	)
December 31, 2015		0.57			(0.53	)

(6) 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."

(7) Amount is less than 0.005%.

(8) Not annualized.

(9) Annualized.

See Notes to Financial Statements
21

Morgan Stanley New York Municipal Money Market Trust

Financial Highlights continued

	FOR THE SIX			FOR THE YEAR ENDED DECEMBER 31,
	MONTHS ENDED
	JUNE 30, 2020			2019			2018			2017			2016⁽¹⁾			2015
	(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		0.004			0.012			0.009			0.002			0.000	⁽²⁾		0.000	⁽²⁾
Less dividends and distributions from net investment income		(0.004	)		(0.012	)		(0.009	)⁽³⁾		(0.002	)		(0.000	)⁽²⁾⁽⁴⁾		(0.000	)⁽²⁾
Net asset value, end of period	$	1.00		$	1.00		$	1.00		$	1.00		$	1.00		$	1.00
Total Return		0.36	%⁽⁹⁾		1.24	%		0.91	%		0.24	%		0.06	%		0.01	%
Ratios to Average Net Assets⁽⁵⁾:
Net expenses		0.17	%⁽¹⁰⁾		0.20	%		0.54	%		0.60	%		0.24	%⁽⁶⁾		0.03	%⁽⁶⁾
Net investment income		0.76	%⁽¹⁰⁾		1.21	%		0.83	%		0.22	%		0.01	%⁽⁶⁾		0.01	%⁽⁶⁾
Rebate from Morgan Stanley affiliate		N/A			N/A			N/A			N/A			0.00	%⁽⁷⁾		0.00	%⁽⁷⁾
Supplemental Data:
Net assets, end of period, in millions	$	4		$	5		$	50	⁽⁸⁾	$	50	⁽⁸⁾	$	50	⁽⁸⁾	$	904

(1) Reflects prior period custodian out-of-pocket expenses that were reimbursed in September 2016. The amount of the reimbursement was immaterial on a per share basis and did not impact the total return of Class S shares. The annualized expense and net investment income ratios would be unchanged as the reimbursement of custodian fees was offset against expense waivers/reimbursements with no impact to the net expenses or net investment income.

(2) Amount is less than $0.001.

(3) Includes paid-in-capital distribution of $0.003.

(4) Includes capital gain and paid-in-capital distributions of less than $0.001.

PERIOD ENDED	EXPENSE RATIO			NET INVESTMENT LOSS RATIO
June 30, 2020		4.78	%		(3.85	)%
December 31, 2019		4.05			(2.64	)
December 31, 2018		2.03			(0.66	)
December 31, 2017		1.79			(0.97	)
December 31, 2016		0.59			(0.34	)
December 31, 2015		0.57			(0.53	)

(7) Amount is less than 0.005%.

(8) In thousands.

(9) Not annualized.

(10) Annualized.

See Notes to Financial Statements
22

Morgan Stanley New York Municipal Money Market Trust

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 Adviser 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 Administrator under the administration agreement, including accounting, operations, clerical, bookkeeping, compliance, business management and planning, legal services and the provision of supplies, office space and utilities at the Adviser's expense. The Board also considered the Adviser's investment in personnel and infrastructure that benefits the Fund. (The Adviser and 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 considered that the Adviser serves a variety of other investment advisory clients and has experience overseeing service providers. The Board also compared the nature of the services provided by the Adviser with similar services provided by non-affiliated advisers as prepared by Broadridge Financial Solutions, Inc. ("Broadridge").

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 advisory and administrative 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 prepared by Broadridge, 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, 2019, or since inception, 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 better than 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 and/or other accounts advised by the Adviser and/or compared to its peers as prepared by Broadridge. In addition to the management fee, the Board also reviewed the Fund's total expense ratio. The Board noted that the Fund's management fee and total expense ratio were lower than its peer group averages. After discussion, the Board concluded

Morgan Stanley New York Municipal Money Market Trust

Investment Advisory Agreement Approval (unaudited) continued

that the Fund's performance, 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 does not include 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/or 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 direct and indirect benefits to the Adviser and/or its affiliates derived from their relationship with the Fund and other funds advised by the Adviser. These benefits may include, among other things, fees for trading, distribution and/or shareholder servicing and for transaction processing and reporting platforms used by securities lending agents, and research received by the Adviser generated from commission dollars spent on funds' portfolio trading. The Board reviewed with the Adviser 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 Board's confidence in the competence and integrity of the senior managers and key

Morgan Stanley New York Municipal Money Market Trust

Investment Advisory Agreement Approval (unaudited) continued

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.

As part of the Board's review, the Board received information from management on the impact of COVID-19 on the firm generally and the Adviser and the Fund in particular including, among other information, the pandemic's current and expected impact on the Fund's performance and operations.

General Conclusion

After considering and weighing all of the above factors, with various written materials and verbal information presented by the Adviser, 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 piece of information or factor referenced above. The Board considered these factors and information over the course of the year and in 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, and the information presented, differently in reaching their individual decisions to approve the Management Agreement.

On June 17, 2020, the Board of Trustees of the Trust approved a Plan of Liquidation with respect to liquidation of the Fund and termination of the Trust. Subject to shareholder approval and pursuant to the Plan of Liquidation, substantially all of the assets of the Fund will be liquidated, known liabilities of the Fund will be satisfied, the remaining proceeds will be distributed to the Fund's shareholders, all of the issued and outstanding shares of the Fund will be redeemed and the Trust will be terminated.

Morgan Stanley New York Municipal Money Market Trust

Privacy Notice (unaudited) April 2019

FACTS				WHAT DOES MSIM DO WITH YOUR PERSONAL INFORMATION?
Why?				Financial companies choose how they share your personal information. Federal law gives consumers the right to limit some but not all sharing. Federal law also requires us to tell you how we collect, share, and protect your personal information. Please read this notice carefully to understand what we do.
What?				The types of personal information we collect and share depend on the product or service you have with us. This information can include: n Social Security number and income n investment experience and risk tolerance n checking account number and wire transfer instructions
How?				All financial companies need to share customers' personal information to run their everyday business. In the section below, we list the reasons financial companies can share their customers' personal information; the reasons MSIM chooses to share; and whether you can limit this sharing.

Reasons we can share your personal information	Does MSIM share?	Can you limit this sharing?
For our everyday business purposes — such as to process your transactions, maintain your account(s), respond to court orders and legal investigations, or report to credit bureaus	Yes	No
For our marketing purposes — to offer our products and services to you	Yes	No
For joint marketing with other financial companies	No	We don't share
For our affiliates' everyday business purposes — information about your transactions and experiences	Yes	No
For our affiliates' everyday business purposes — information about your creditworthiness	No	We don't share
For our affiliates to market to you	No	We don't share
For non-affiliates to market to you	No	We don't share

Questions? Call toll-free (844) 312-6327 or email: imprivacyinquiries@morganstanley.com

Morgan Stanley New York Municipal Money Market Trust

Privacy Notice (unaudited) continued April 2019

Who we are

Who is providing this notice?

Morgan Stanley Investment Management, Inc. and its affiliated registered investment advisers, registered broker-dealers, and registered and unregistered funds ("MSIM")

What we do

How does MSIM protect my personal information?				To protect your personal information from unauthorized access and use, we use security measures that comply with federal law. These measures include computer safeguards and secured files and buildings. We have policies governing the proper handling of customer information by personnel and requiring third parties that provide support to adhere to appropriate security standards with respect to such information.
How does MSIM collect my personal information?				We collect your personal information, for example, when you n open an account or make deposits or withdrawals from your account n buy securities from us or make a wire transfer n give us your contact information We also collect your personal information from others, such as credit bureaus, affiliates, or other companies.
Why can't I limit all sharing?				Federal law gives you the right to limit only n sharing for affiliates' everyday business purposes — information about your creditworthiness n affiliates from using your information to market to you n sharing for non-affiliates to market to you State laws and individual companies may give you additional rights to limit sharing. See below for more on your rights under state law.

Morgan Stanley New York Municipal Money Market Trust

Privacy Notice (unaudited) continued April 2019

Definitions

Affiliates				Companies related by common ownership or control. They can be financial and non-financial companies. n Our affiliates include companies with a Morgan Stanley name and financial companies such as Morgan Stanley Smith Barney LLC and Morgan Stanley & Co.
Non-affiliates				Companies not related by common ownership or control. They can be financial and non-financial companies. n MSIM does not share with non-affiliates so they can market to you.
Joint marketing				A formal agreement between non-affiliated financial companies that together market financial products or services to you. n MSIM doesn't jointly market

Other important information

Vermont: Except as permitted by law, we will not share personal information we collect about Vermont residents with Non-affiliates unless you provide us with your written consent to share such information.

California: Except as permitted by law, we will not share personal information we collect about California residents with Non-affiliates and we will limit sharing such personal information with our Affiliates to comply with California privacy laws that apply to us.

Trustees

Frank L. Bowman

Kathleen A. Dennis

Nancy C. Everett

Jakki L. Haussler

Dr. Manuel H. Johnson

Joseph J. Kearns

Michael F. Klein

Patricia Maleski

W. Allen Reed, Chair of the Board

Officers

John H. Gernon
President and Principal Executive Officer

Timothy J. Knierim
Chief Compliance Officer

Francis J. Smith
Treasurer and Principal Financial Officer

Mary E. Mullin
Secretary

Michael J. Key
Vice President

Transfer Agent

DST Asset Manager Solutions, 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

Perkins Coie LLP
1155 Avenue of the Americas,
22nd Floor
New York, New York 10036

Adviser and Administrator

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) 548-7786.

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.

DWNSAN
3186605 EXP. 08.31.21

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.

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

There have been no material changes to the procedures by which shareholders may recommend nominee to the Fund’s Board of Trustees since the Fund last provided disclosure in response to this item.

Item 11. Controls and Procedures

(a) The registrant’s principal executive officer and principal financial officer have concluded that the registrant’s disclosure controls and procedures are sufficient to ensure that information required to be disclosed by the registrant 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 most recent fiscal half-year 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. Disclosure of Securities Lending Activities for Closed End Management Investment Companies.

Not Applicable.

Item 13. 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.

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/John H. Gernon
John H. Gernon
Principal Executive Officer
August 13, 2020

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/ John H. Gernon
John H. Gernon
Principal Executive Officer
August 13, 2020

/s/ Francis Smith
Francis Smith
Principal Financial Officer
August 13, 2020

Date:August 13, 2020
	/s/ John H. Gernon
	John H. Gernon
	Principal Executive Officer

Date: August 13, 2020
	/s/ Francis Smith
	Francis Smith
	Principal Financial Officer