New Mexico Statutes Chapter 39. Judgments, Costs, Appeals § 39-3-4. Interlocutory order appeals from district court

A. In any civil action or special statutory proceeding in the district court, when the district judge makes an interlocutory order or decision which does not practically dispose of the merits of the action and he believes the order or decision involves a controlling question of law as to which there is substantial ground for difference of opinion and that an immediate appeal from the order or decision may materially advance the ultimate termination of the litigation, he shall so state in writing in the order or decision.

B. The supreme court or court of appeals has jurisdiction over an appeal from such an interlocutory order or decision, as appellate jurisdiction may be vested in those courts.  Within fifteen days after entry of the order or decision, any party aggrieved may file with the clerk of the supreme court or court of appeals an application for an order allowing an appeal, accompanied by a copy of the interlocutory order or decision.

C. Application under this section for an order allowing appeal does not stay proceedings in the district court unless so ordered by the district judge or a judge or justice of the court to which application is made.