This appears to be the first true "whodunit" of The CBS Radio Mystery Theater.  Thanks to the nature of radio, we can hear the murder, but we can't see the killer.  As is generally the case with murder mysteries, the victim is unsympathetic and there are a lot of players with motive.  Solution does not hinge on the discovery of clever clue or on logical deduction, but by a breakdown confession of the killer.  Murder mystery, no supernatural elements.