Okay, so let's say someone tries to rape my wife in a non-police state. I attack him in defense. He claims I tried to rape his wife instead. Without police, who is going to investigate? If the investigation is done by "peers", who said those peers aren't corrupt? I guess the real purpose of a police state is to keep everyone from being subject to corruption (ironic that it does exactly the opposite)
There would be investigators. They might even wear blue costumes. They just wouldn't have a monopoly on the job.