The Man in the Back Seat [1961] [DVD]

Two young thugs rob a bookie leaving a dog-racing track with his winnings, but when they grab his case full of money they discover that he has chained it to his wrist. They dash around town trying to find a way to separate the case from the wrist of the bookie, who the pair has by now beaten so badly he appears to be dead. They finally come up with what they think is a foolproof plan, but soon something happens that they weren't quite expecting.