N.M. Stat. § 40-11A-642
Notwithstanding any other laws concerning public hearings and records, any hearing or trial held under the provisions of the New Mexico Uniform Parentage Act may be held in closed court without admittance of any person other than those necessary to the action or proceeding. The court may order that certain papers and records pertaining to the action or proceeding, whether part of the permanent record of the court or any other file maintained by the state or elsewhere, are subject to inspection only upon consent of the court; provided, however, that nothing in this section shall infringe upon the right of the parties to an action or proceeding to inspect the court record. The provisions of this section are subject to any rules established by the New Mexico supreme court.
NMS § 40-11A-642