N.M. Stat. § 38-3-9
Peremptory challenge to a district judge.
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.