OK, guys. Homicide isn't
a crime. Homicide is the killing of one human being by another. It may be accidental or on purpose, and may be criminal in either case (negligent homicide, involuntary manslaughter, manslaughter, murder). If a homicide is justifiable or excusable (the difference is really moot) then the slayer has committed no crime. However, in all but the most blatent cases of self-defense, it is likely that the slayer will be arrested and possibly charged with murder, manslaughter, or some similar crime.
Getting back to the original question, there is nothing in the law that requires you to notify police or anyone else if you shoot someone in self-defense. However
it is almost always in your best interests to do so. Failure to report the incident, and leaving the scene can be construed as flight to avoid prosecution, and may well convince a jury that the shooting was not really in self-defense. Moreover, if, by failing to report the shooting, the "victim" dies when (s)he otherwise might have been saved by timely medical treatment, you may, indeed, be guilty of negligent homicide or involuntary manslaughter, depending on statutes.