Application to the supreme court for writ of certiorari to the court of appeals shall be filed with the clerk of the supreme court within twenty days after final action by the court of appeals. A copy of the application shall be filed by the clerk of the supreme court with the clerk of the court of appeals and the clerk of the court of appeals shall forthwith transmit the record in the case to the clerk of the supreme court. Upon filing of the application, the judgment and mandate of the court of appeals shall be stayed pending final action of the supreme court. No further briefs or oral argument in support of an application for writ of certiorari shall be filed or had in the supreme court unless so directed by the supreme court. If an application has not been acted upon within thirty days, it shall be deemed denied.
Any certification by the court of appeals under this subsection is a final determination of appellate jurisdiction.
NMS § 34-5-14