N.M. Stat. § 62-11-2
Upon the filing of a notice of appeal, the appellant shall cause a copy thereof to be served upon the commission and parties of record in the proceeding before the commission in the manner prescribed by the Rules of Appellate Procedure for Civil Cases. Within thirty days after service of the notice of appeal or such further time as the supreme court for good cause may specify, the commission shall certify to the supreme court the record of the testimony taken before the commission and all exhibits offered or received in evidence at the hearing before the commission, and all pleadings, findings, conclusions, orders and opinions, or certified copies thereof, made and entered in, or in connection with, the hearing before the commission; provided, however, that the parties and the commission may stipulate that a specified portion only of the testimony taken at the hearing before the commission shall be certified to the supreme court for review on appeal.
NMS § 62-11-2