Here we go again.
My understanding is this.
If you display your weapon and dont fire it... as long as you believed that you would have been justified in using it, and in fact you would have been justified.... No crime has been commited. But the police may see it differently.
If you fire your gun at a human, and strike that human, and that Human dies as a result of that gunshot, that would be a homicide. A grand jury, or coronors jury, or a judge at a felony hearing may rule the shooting a reckless homicide, a criminally neglegent homicide, a justified homicide, an accident, or some degree of murder.
A justifiable homicide requires an affermative defense. In order to claim justification you must admit that you fired the shot. An affermative defense shifts the burden of proof from the state to the subject. With the same standard of proof. "BEYOND A REASONABLE DOUBT".
The decision of talking to the police at the scene is personal, and should not be taken lightly. I'm sure a lot of folks will chime in with good advice for talking or not talking.
This information is based on criminal law from the state of NY. Every state has their own criminal law, and may differ from state to state.