Post-Conviction DNA Testing Act of 2002 - Amends the Federal criminal code to establish procedures for post-conviction DNA testing. Authorizes an individual imprisoned because of a conviction of a criminal offense in a U.S. court to make a written motion to the court for the performance of forensic DNA testing on specified evidence.

Sets forth requirements regarding: (1) the substance of the motion (including an assertion of innocence of the crime if exoneration would result in a mandatory sentence reduction) and the timing of its filing (within 60 months); (2) notice to the Government, the preservation order, and appointment of counsel; (3) the order for DNA testing; (4) testing and result reporting procedures; (5) post-testing procedures where test results are inconclusive, positive, or negative or produce exculpatory evidence; and (6) finality of an order granting or denying DNA testing or a new trial.

Prohibits the Government from destroying any biological material preserved if the defendant is serving a term of imprisonment following conviction in a case until the later of: (1) 60 months after enactment of this Act; or (2) the date DNA testing proceedings are completed.

Directs the Attorney General to establish a system for reporting and tracking motions under this Act. Prohibits a State from denying an application for DNA testing made by a prisoner in State custody who would be eligible for such testing under Federal provisions pursuant to this Act. Authorizes a prisoner in State custody to enforce such provision in a civil action for declaratory or injunctive relief.