Two Letter Alibi(1962)

Charles Hilary is in love with Kathy Forrester, a beautiful television personality, but is married to Louise, an alcoholic with as many lovers as whisky bottles. His pleas for a divorce are met with threats and abuse. "You'll have to murder me first", Louise tells him and three hours later she is found dead, shot with her husband's pistol. When Charles is arrested, Kathy desperately sets to work to prove his innocence.