N.M. Stat. § 52-3-41
Any employee to whom compensation has been allowed or awarded who desires to leave the locality in which he was employed shall report to his attending physician for examination and shall notify the director in writing of his intention, accompanying the notice with a certificate from the attending physician setting forth the exact nature of the disablement and the condition of the employee with a statement of the probable length of time the disablement will continue. The director may, after the receipt of the request and certificate, consent that the employee leave the locality and give notice thereof to the employer. Otherwise, no compensation shall be paid during such absence. The director shall have the authority to order any employee to return for treatment or further examination to the locality in which he was employed, and in the event of noncompliance with the order, no further payments of compensation shall be made by the employer.
NMS § 52-3-41