The police can talk to whoever they like. Illegally search, beat up, and arrest for murder? Not so much.
Oswald made an arrest legal by taking the first punch (as Brewer testified). No one had a clue if he had shot anyone at that point (if some did, by all means do post that info).
Try to keep up: The police were dispatched to cover all reports of suspicious-looking activity as seen
by alert citizens. It was a manhunt, FFS.