N.M. Stat. § 59A-15-6
Any act of transacting an insurance business in this state by any unauthorized insurer is equivalent to and shall constitute an irrevocable appointment by such insurer, binding upon him, his executor or administrator, or successor in interest if a corporation, of the superintendent or his successor in office, to be the true and lawful attorney of the insurer upon whom may be served all lawful process in any action, suit or proceeding in any court by the superintendent or by the state or others, and upon whom may be served any notice, order, pleading or process in any proceeding before the superintendent, and which arises out of transacting an insurance business in this state by such insurer. Any act of transacting an insurance business in this state by any unauthorized insurer shall be signification of its agreement that any such lawful process in such court action, suit or proceeding and any such notice, order, pleading or process in such administrative proceeding before the superintendent so served shall be of the same legal force and validity as personal service of process in this state upon the insurer.
NMS § 59A-15-6