I am not sure of specific laws, but I'm sure there are some as far as reporting an injured person or a dead body. You do not have to admit to doing the shooting when you call, just say someone has been shot and they need an ambulance. In VA to use self defense as a defense you have to admit to manslaughter. In most cases you are certainly better off saying this is the bad guy and I feared for my life, then request a lawyer before giving any details.
If you do not admit to shooting the dead person they would have to prove you did. How that would effect a later self defense claim I do not know.