The Alfred Hitchcock Hour (1962)

S2E4 You'll Be the Death of Me

In the heat of a passionate argument, Dandy Arthur ends up killing his former girlfriend. Amid the chaos, a button from her coat gets lodged in his pocket. When his wife discovers the button, Dandy decides he must eliminate her too. However, as he talks excessively, he inadvertently reveals too much, leading to his arrest by the police.