Both of my suppositions presuppose that Oswald thought he had a bit of help. Of course, it could just be that he was a loser who worked himself up to shooting at the President, and once that was done, had no further goal and drifted in a daze until shooting Officer Tippit. And after that, had a breakdown and looked for the nearest dark hole he could find, the Texas Theater, a 1/2 mile away. That seems entirely possible, and I stress, is the most likely solution. While there were a LOT of peculiarities surrounding the JFK assassination (For one, how does the same guy who blows the shot at General Walker, make two hits on a ~70 yd. moving target within a few seconds?) I find it most likely that Oswald acted alone. To me, any activities smelling of coverup were the result of stress-induced incompetence and the perceived need for rapid finality in the investigation.
If however, you think that Oswald thought he had help, then for me it depends if you believe Garrison’s allegations that two other people shot Tippit. If you disbelieve Garrison—as most people do—and think Oswald shot Officer Tippit, then retrace Oswald’s path between his room at 1026 N. Beckley, to Tippit’s death at 10th Street near Patton Avenue. If you extend the path a little further, it sort of points to the Dallas Zoo. I can see the Zoo being a decent spot for a meet with Oswald walking to the Zoo as fast as he could, thinking he was going to meet his handler, get a fake ID/passport, cash, transport, that sort of thing. Shooting Tippit causes Oswald to wig out/think he’s been set up, and run to the theater.
If you believe Garrison, then “other people” shot Tippit while Oswald is sitting fat, dumb, and happy in the Texas Theater. Either he’s killing time or he’s having the meet in the Theater. I don’t buy this at all, given that Oswald tried to get into the Theater without paying—what better way to act low-key? Further, he acted so furtively and guilty on the way to the Theater that a shoe store manager, Johnny Brewer, noticed and decided to follow Oswald. All that says to me that Oswald was acting on adrenaline and wasn’t thinking, just like someone would be acting if they’d just shot a Dallas policeman.
So to sum up, he was in a daze from shooting JFK, went home, figured out that was a dumb place to be, and was wandering around until Tippit runs into him. Or, if you’re conspiracy-minded, he was hoofing it to make his meet at the Dallas Zoo, until Tippit runs into him…