I've reproduced the Alabama statute below. For you guys who like "angels on the head of a pin" questions, the answer is "yes." However, the fact that there are no appealed cases on it should tell you all you need to know. The miseries it could cause one, real life problems - not theoretical ones - have been mostly touched on in this thread. To a lawyer, there are even more. The real answer is to record and become a witness. But to answer the theoretical question, there's no blanket prohibition against a citizen's arrest on an LEO that I know of (but I'm not a criminal lawyer, after all). Here is the statute:
Section 15-10-7 of the Code of Alabama reads as follows:
Arrests by private persons.
(a) A private person may arrest another for any public offense:
(1) Committed in his presence;
(2) Where a felony has been committed, though not in his presence, by the person arrested; or
(3) Where a felony has been committed and he has reasonable cause to believe that the person arrested committed it.
(b) An arrest for felony may be made by a private person on any day and at any time.
(c) A private person must, at the time of the arrest, inform the person to be arrested of the cause thereof, except when such person is in the actual commission of an offense, or arrested on pursuit.
(d) If he is refused admittance, after notice of his intention, and the person to be arrested has committed a felony, he may break open an outer or inner door or window of a dwelling house.
(e) It is the duty of any private person, having arrested another for the commission of any public offense, to take him without unnecessary delay before a judge or magistrate, or to deliver him to some one of the officers specified in Section 15-10-1, who must forthwith take him before a judge or magistrate.
Now, I'm sure all know how to do all these things...