If a person shoots and kills a bad guy in self defense, does the law require the shooter to turn himself in to the police?
That is a two pronged question; First, If you shoot and kill anyone
(statutorily, Homicide) has
been committed. I would think, in almost every State you would be required to report that the incident occurred.
Second; whether you " turn yourself in" would depend greatly on the circumstances, and what information you
volunteer to the investigating authorities once they arrive.
In an "affirmative defense" you are admitting
that you committed the homicide. Thus, you have waived at least part
of your 5th amendment rights in order to mount your defense.
As to the question of whether it was a justified
homicide, that will be hashed out by the authorities in that jurisdiction.