§ 38-3-9 NMSA 1978

A party to an action or proceeding, civil or criminal, including proceedings for indirect criminal contempt arising out of oral or written publications, except actions or proceedings for constructive and other indirect contempt or direct contempt shall have the right to exercise a peremptory challenge to the district judge before whom the action or proceeding is to be tried and heard, whether he be the resident district judge or a district judge designated by the resident district judge, except by consent of the parties or their counsel. After the exercise of a peremptory challenge, that district judge shall proceed no further. Each party to an action or proceeding may excuse only one district judge pursuant to the provisions of this statute. In all actions brought under the Workmen's Compensation Act ( 52-1-1 to 52-1-69 NMSA 1978) [Workers' Compensation Act (Chapter 52, Article 1 NMSA 1978)], the employer and the insurance carrier of the employer shall be treated as one party when exercising a peremptory challenge to the judge under this statute. The rights created by this section are in addition to any arising under Article 6 of the constitution of New Mexico.