N.M. Stat. § 32A-1-17

A. Any party may appeal from a judgment of the court to the court of appeals in the manner provided by law. The appeal shall be heard by the court of appeals upon the files, records and transcript of the evidence of the court. Absent an order of the appellate court, files and records that are required to be kept confidential and closed to the public, pursuant to any provision of the Children's Code shall be kept confidential and closed to the public on appeal.

B. The appeal to the court of appeals does not stay the judgment appealed from, but the court of appeals may order a stay upon application and hearing consistent with the provisions of the Children's Code if suitable provision is made for the care and custody of the child. If the order appealed from grants the legal custody of the child to or withholds it from one or more of the parties to the appeal, the appeal shall be heard at the earliest practicable time.

C. If the court of appeals does not dismiss the petition and order the child released, it shall affirm the court's judgment or it shall modify the court's judgment and remand the child to the jurisdiction of the court for disposition consistent with the appellate court's decision on the appeal. Any party may appeal to the supreme court in the manner provided by law.

D. A child who has filed notice of appeal shall be furnished a transcript of the proceedings, or as much of it as is requested, without cost upon the filing of an affidavit that the child or the person who is legally responsible for the care and support of the child is financially unable to purchase the transcript.

E. Appeals from the court to the court of appeals shall proceed in accordance with time limits to be established by the supreme court.

F. Appeals from a tribal court order shall proceed pursuant to tribal law to an appropriate tribal court.