Fugitive Apprehension Act of 2001 - Amends the Federal criminal code to authorize the Attorney General to subpoena witnesses for the purpose of the production of any records that the Attorney General finds, based on articulable facts, are relevant to discerning the whereabouts of a fugitive. Specifies that the attendance of witnesses and the production of records may be required from any place in any State or other place subject to U.S. jurisdiction, except that a witness shall not be required to appear more than 500 miles from the place where the witness was served.

Sets forth provisions regarding service of process and contumacy or refusal to obey a subpoena.

Directs the Attorney General to issue guidelines governing the issuance of administrative subpoenas.

Authorizes the Attorney General to apply to a court for an order requiring the party to whom an administrative subpoena is directed to refrain from notifying any other party of the existence of the subpoena or court order. Directs the court to enter such order if it determines that there is reason to believe that notification of the existence of the subpoena will result in: (1) endangering life or physical safety: (2) flight from prosecution; (3) destruction of or tampering with evidence; (4) intimidation of potential witnesses; or (5) otherwise seriously jeopardizing an investigation or undue delay of a trial.

Grants immunity from civil liability to persons who in good faith produce records or items requested in a subpoena.