Would it be in my best interest to, after said NG, call the local police and let them know what happened? Would they probably still show up If I did this? They do know who I am and know that I own guns. We are on friendly terms.
Common sense says that IF your firearm was discharged accidentally, and the police didn't arrive contemporaneously with the alleged incident, to follow the Clinton doctrine of DA, DT (don't ask, don't tell).
If no one was injured (or, God forbid KILLED) after the incident, no harm, no foul.
The police are a very busy lot.
I don't know of many police agencies investigating misdemeanors (absent injury, property loss, or theft) days after the alleged incident occurred.
Hypothetically, had this occurred 48 hours ago, I doubt the police will come calling tomorrow.
If they did, such an incident would be impossible to prove.
In NC LEOs are only able to make an arrest absent a warrant for the following:
shoplifting,
DUI,
domestic criminal trespass,
violation of a 50B (domestic protective order),
violating a pre-trial release order (stalking, staying away from they're home, phoning, emailing...etc.),
assault by pointing a gun (if in a relationship with one another),
assault on a female,
assault inflicting serious injury or assault w/deadly weapon.
Otherwise a magistrate must sign off via a warrant.