We don’t know where Oswald was headed when he was stopped by Officer Tippit. But he panicked then and killed Tippit with his .38. He then headed through a business district where people noticed him and saw him flee into the theater. They directed police into the theater where Oswald attempted to shoot them as well.
Some patsy.
Oswald was a freaking nut case who didn’t think things trough. He operated on impulse like the majority of criminals do.
Tippet was killed by G. Gordon Libby