North Carolina does not have a "Citizens Arrest". A citizen has the authority to detain a person who commits a crime in their presence until the cops are called. But like Jim said, we also have a false imprisonment law. Prohibiting someone from leaving is a crime unless they have broken the law. In my opinion, there is just too much gray areas and "what if's" in there.
G.S. 15A-404 Detention of offenders by private persons.
No Arrest; Detention Permitted. - No private person may arrest another person except as provided in G.S. 15A-405 [assisting law enforcement officers in making an arrest.] A private person may detain another person as provided in this section.
A private person may detain another person when he has probable cause to believe that the person detained has committed in his presence:
(1) A felony,
(2) A breach of the peace,
(3) A crime involving physical injury to another person, or
(4) A crime involving theft or destruction of property.
(c) Manner of Detention. - The detention must be in a reasonable manner considering the offense involved and the circumstances of the detention.
(d) Period of Detention. - The detention may be no longer than the time required for the earliest of the following:
(1) The determination that no offense has been committed.
(2) Surrender of the person detained to a law enforcement officer as provided in subsection (e).
(e) Surrender to Officer. - A private person who detains another must immediately notify a law enforcement officer and must, unless he releases the person earlier as required by subsection (d), surrender the person detained to the law enforcement officer.
In the beginning, the patriot is a scarce man -- brave, hated, and scorned. But when his cause succeeds, the timid join him. For then, it costs nothing to be a patriot. -- Mark Twain