Ala. Code § 36-21-128: Limitation of Powers.

The power of a police officer employed by the tribe pursuant to this article may be exercised only upon the reservation, and a police officer may not otherwise act as a police officer off of the reservation except under either of the following conditions:

(1) When lawfully pursuing any offender suspected of committing an offense while on the reservation.

(2) When making an arrest for a felony that has been committed either in the presence of the police officer or, where probable cause exists, on the reservation.