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.