I don't care if he did "assualt" a cop or if his hands were up or how many convenience stores he robbed... once the individual is not actively attacking you, you have NO LEGAL GROUNDS for use of lethal force. Consider it in the context of a civilian. Would a legal gun owner be able to shoot a fleeing perpetrator who assaulted him and not end up in jail? ... No he would end up in a cage regardless of what the suspect did. Police have no additional rights above any other citizen regardless of how much they think they do.
This is true however there is evidence to suggest that Brown was still actively attacking the police officer when he was shot. He may have been in-between punches however there is evidence that he was shot at very close range and that he may have been reaching for the officer's gun