American Servicemembers' Protection Act of 2001

American Servicemembers' Protection Act of 2001 - Prohibits U.S. cooperation with the International Criminal Court. Specifies restrictions on: (1) participation by covered U.S. persons in United Nations (UN) peacekeeping and peace enforcement operations; (2) transfer to the Court of U.S. classified national security and law enforcement information; and (3) the provision of U.S. military assistance, with specified exceptions, to the government of a country that is a party to the Court.

Prescribes conditions for a presidential waiver of the prohibitions and requirements of this Act.

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; or (2) communication by the United States of its policy with respect to a matter.

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

Urges the President to report to appropriate congressional committees on the degree to which: (1) each military alliance to which the United States is a party may place U.S. armed forces under foreign control subject to the Court's jurisdiction; and (2) 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.

Expresses the sense of Congress that the President should rescind the signature made on behalf of the United States to the Rome Statute of the International Criminal Court, adopted by the UN Diplomatic Conference of Plenipotentiaries on the Establishment of an International Criminal Court on July 17, 1998.