Now let's look at this another way.
Originally Posted by Skans
...It seems contradictory to me that you can be required by law to report a shooting, which may or may not be later determined to have been done in self defense. This seems contrary to the protections of the 5th Amendment....
Maybe there are no laws requiring that you report it, or if there are you successfully avoid liability under one by pleading the 5th Amendment.
However, the practical effect of not reporting the event is that you have substantially increased the likelihood that your self defense claim will fail. So you won't go to jail for a failure to report. You'll be convicted of aggravated assault or manslaughter, depending on whether your victim lives or dies.