In the U.S., the Police don't need a warrant under certain conditions, including exigent circumstances. As for police use of deadly force, the current threshold in Washington state is "good faith" and "without malice". There's some effort under way by the state to tighten down the requirements to be what a "reasonable officer" might do under the circumstances. But it's a difficult issue to get right. I'm skeptical that the officers in question were behaving badly.