Dead Ringer
(1964)

Maggie and Edith are twins (both played by Bette Davis).  Edith was in love with super wealthy Frank.  Maggie seduced Frank, then claimed to be pregnant so he had to marry her (it was the 1940s).   Maggie never loved him, but loved the super rich lifestyle.  The two sisters did not speak for 20 years, until Edith went to Frank's funeral.  Edith learns it was a lie, Maggie was never pregnant.

Edith lures Maggie to her home.  Edith kills Maggie, switches clothes and leaves a suicide note.  Everyone thinks it is Edith dead.  Edith assumes Maggie's wealthy lifestyle.  Maggie's lover, Tony, returns from Europe and realizes the switch.  He begins to blackmail Edith.  In a stroke of luck for Edith, her Great Dane sees Tony menacing her.  The dog kills Tony.

Edith's boyfriend, Sergeant Hobbson (Karl Malden) knows something is up.  As a police officer, he investigates Tony and Maggie.  He finds proof that Tony and Maggie murderd Frank with arsenic.  Edith (living as Maggie) is tried for murder and sentenced to death.  She is trapped, because if she reveals that she is really Edith then she will still be guilty of Maggie's murder. 

Thanks Joseph C!