American Servicemembers' Protection Act of 2001

American Servicemembers' Protection Act of 2001 - Prohibits U.S. cooperation with the International Criminal Court (including specified restrictions on U.S. military participation in United Nations (UN) peacekeeping and peace enforcement operations, transfer of U.S. classified national security information, and the provision of U.S. military assistance, with specified exceptions, to the Court and its members).

Prescribes conditions for a presidential waiver of the prohibitions and requirements of this Act. Terminates such prohibitions and requirements upon the United States' becoming a party to the Court.

Declares that the requirements of this Act shall not prohibit: (1) any action authorized by the President to bring about the release from captivity of any U.S. military personnel (covered U.S. persons) and certain other persons (covered allied persons) who are being detained or imprisoned against their will by or on behalf of the Court; (2) any other action taken by U.S. armed forces outside of the United States while engaged in military operations involving the threat or use of force to protect such personnel from harm or to ensure the success of such operations; or (3) communication by the United States to the Court of its policy with respect to a particular matter.

Authorizes the President to use all means (including the provision of legal assistance) necessary to bring about the release of covered U.S. persons and covered allied persons held captive by or on behalf of the Court.

Directs the President to report to appropriate congressional committees with respect to each military alliance to which the United States is a party: (1) describing the degree to which U.S. armed forces may be placed pursuant to the alliance under foreign control subject to the jurisdiction of the Court; and (2) evaluating the degree to which U.S. armed forces engaged in military operations pursuant to such alliance may be exposed to greater risks as a result of being placed under such foreign control.

Authorizes funds withheld from the U.S. share of assessments to the UN or other international organizations pursuant to the Admiral James W. Nance and Meg Donovan Foreign Relations Authorization Act, Fiscal Years 2000 and 2001 to be transferred to the Embassy Security, Construction and Maintenance Account of the Department of State.