N.M. Stat. § 62-10-16
After an order or decision has been made by the commission, any party to the proceedings, may within thirty days after the entry of the order or decision apply for a rehearing in respect of any matters determined in said proceedings and specified in the application for rehearing, and the commission may grant and hold such rehearing on said matters. The commission shall either grant or refuse an application for rehearing within twenty days after the application therefor is filed in the office of the commission; and a failure by the commission to act upon such application within that period shall be deemed a refusal thereof. If the application be granted, the commission's order shall be deemed vacated, and the commission shall enter a new order after the rehearing shall have been concluded.
NMS § 62-10-16