California is fairly straightfoward - From the Penal Code -
834. An arrest is taking a person into custody, in a case and in the manner authorized by law. An arrest may be made by a peace officer or by a private person.
and
837. A private person may arrest another:
1. For a public offense committed or attempted in his presence.
2. When the person arrested has committed a felony, although not in his presence.
3. When a felony has been in fact committed, and he has reasonable cause for believing the person arrested to have committed it.
839. Any person making an arrest may orally summon as many persons as he deems necessary to aid him therein.
847. (a) A private person who has arrested another for the
commission of a public offense must, without unnecessary delay, take
the person arrested before a magistrate, or deliver him or her to a
peace officer.
(b) There shall be no civil liability on the part of, and no cause
of action shall arise against, any peace officer or federal criminal
investigator or law enforcement officer described in subdivision (a)
or (d) of Section 830.8, acting within the scope of his or her
authority, for false arrest or false imprisonment arising out of any
arrest under any of the following circumstances:
(a) The arrest was lawful, or the peace officer, at the time of
the arrest, had reasonable cause to believe the arrest was lawful.
(b) The arrest was made pursuant to a charge made, upon reasonable
cause, of the commission of a felony by the person to be arrested.
(c) The arrest was made pursuant to the requirements of Section
142, 837, 838, or 839.