It depends on the state.

In Texas, the district attorney can choose to recommend a charge to the grand jury. But even if he does not do so, every homicide is reviewed by a grand jury.

The grand jury decides whether there is evidence of a crime and issues an indictment (true bill, I think), or not (no bill). If they issue an indictment, then it goes to a trial jury, who decides whether the homicide was a justifiable use of deadly force.

Moral of this story: once you pull the trigger in self-defense, you are looking at a large legal bill, even if it's an open-and-shut case.