h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

In "Forgotten Lady" Janet Leigh's character murders Sam Jaffee's character and does (sort of get away with it). It turns out that her character has a rare, deadly brain disease which will kill her within a few short months, and which has most likely already led to her forgetting that she was the one who killed him. The reason (in her mind) is that he refused to support her in trying to restart her musical career on the stage, not knowing that the strain (due to her condition) would probably kill her outright.

John Payne's character confesses to the crime (knowing that he will be found to be innocent and released) so that Ms. Leigh's character can spend her short remaining time secure in the knowledge that her husband's murderer has been caught. Her character, to my knowedge, is the only one to ever avoid capture. Columbo reasons that she is dying, her condition probably led to her following the impulse to kill, and she has even forgotten that she was the one who did it, so he allows her to die in peace.