Here's what I found:

"When Tippit got out of his patrol car, Oswald suddenly pulled out a pistol and shot Tippit four times, killing him instantly. Two people witnessed the shooting and later identified Oswald as Tippit's killer, and seven others saw Oswald running from the scene, carrying a pistol. Oswald was arrested in a nearby movie theater when the ticket seller called police about a suspicious looking man. When arrested, Oswald still had the .38 cal. Pistol on him that he used to kill Tippit, and later ballistics tests identified that pistol as the gun that killed Tippit."

Taken from here.