N.M. Stat. § 77-13-7
Upon the impoundment of any estray animal or animals as provided in Section 77-13-2 NMSA 1978, the impounder shall be entitled to hold same lawfully until relieved of their custody by the New Mexico livestock board. Should a claimant for the animal or animals apply to the impounder for possession of the same, the impounder shall at once notify the New Mexico livestock board in writing of such application. Should the board be satisfied that the applicant is the lawful owner, it shall forthwith issue an order by the director authorizing the impounder to deliver said estray or estrays to the owner, who may be required to pay any reasonable charges incurred by the impounder; provided, that in case of a controversy as to what shall constitute a reasonable charge, the New Mexico livestock board shall fix the amount, the time of service for which the impounder may claim remuneration, commencing on the date of notification made by the impounder to the New Mexico livestock board.
NMS § 77-13-7