The Killers
(1946)

The contract killing of Burt Lancaster at the beginning of the film is because he doublecrossed his partners in a payroll heist. He was then doublecrossed by the femme fatale Ava Gardner.

The insurance investigator (Edmond O'Brien) solves the mystery and has Ava sent to the slammer.  

Thanks Don P!

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Read more about this film at The Internet Movie Database.