You should mutilate the body so the police can identify it, and then spray your house down with bleech (yea this advice is kinda late), and then you should get out of town, because if your reading this you had time to do that.
This is actually an interesting hypothetical situation. What would I do if I shot a policeman in self defense? The judge will obviously say it's manslaughter or even first-degree.
A person in the US today who moves away from were they were - picks up a new ID and has no contact with their old life really has only a small chance of being caught