Habeas Corpus Procedures Amendments Act of 1981 - Prohibits Federal magistrates from conducting evidentiary hearings in habeas corpus actions brought by State prisoners.

Prohibits the consideration in a habeas corpus proceeding of a Federal question which was not properly presented under State law at trial and on appeal unless the petitioner establishes that the alleged violation of the Federal right was prejudicial and that: (1) the Federal right did not exist at time of trial and has been determined to be retroactive; (2) the State procedures precluded assertion of the right; (3) evidence was suppressed which prevented raising of the claim; or (4) material and controlling facts upon which the claim is based were unknown and could not have been ascertained by reasonable diligence.

Establishes a three-year statute of limitations for habeas corpus actions brought by State prisoners.

Prohibits the Federal evidentiary hearing from being conducted where State court records contain factual findings, unless the petitioner establishes the existence of at least one of six enumerated circumstances. (Currently, the State findings are presumed to be correct unless petitioner establishes existence of a circumstance.) Eliminates from such circumstances that the applicant: (1) did not receive a full, fair, and adequate hearing; or (2) was otherwise denied due process.