In north Carolina there is no citizen's arrest. There is a limited right to detain, but it is unclear even to most ccw trainers. there are penalties for unlawful detainment. It is never legal, even fo an LEO, to use deadly force to detain anyone. It is probably a very good thing that most criminals don't know this. In NC., as well as most other states, if a felony suspect gets up off the ground, turns his back and walks away, the officer has no standing under the law to shoot. You can not use deadly force to detain a suspect, law enforcement or private citizen. As I say, it is probably as good thing most thugs don't know this. It would put an officer in the uncomfortable situation of having to holster their weapon and tackling a three hundred pound drug thug.
For all practical intents and purposes, you have no right to detain any one, no matter what they have done, for any reason, for any length of time. If they are willing to leave, let themn leave. Especially if you have to point a gun at them to hold them. If you can manhandle them without risk to yourself, as i did once, you probably won't gret into trouble. if you pull your pistol, and they turn out to be innocent, tyhemn you have committied assault with a deadly weapon at least, and possibly kidnapping, if they were removed from one place tro another. Unlawful detainment is another thing, as is unlawful detainment of a minor. Let them leave, and try to remember what they looked like. Even law enforcement agencies give this advice to off duty officers. You have got to understand that pointing a pistol is deadly force. Shooting at someone without hitting them is deadly force. Shooting them in the leg is deadly force. You simply are not jistified doing any of these things unless your life is in immediate danger.