A former U.S. Marine who had defected to live in the Soviet Union for almost 3 years , Oswald was initially arrested in the death of police officer J. D. Tippit , who had been shot on a Dallas street shortly after Kennedy was killed . A former U.S. Marine who had briefly defected to the Soviet Union , Oswald was initially arrested for the shooting murder of police officer J. D. Tippit , on a Dallas street approximately 40 minutes after Kennedy was shot .