N.M. Stat. § 59A-37-10
The courts of this state are hereby vested with jurisdiction over any person not resident, domiciled or authorized to do business in this state, who files a statement with the superintendent under Sections 619 through 622 [59A-37-4 to 59A-37-7 NMSA 1978] of this article, and over all actions involving such person arising out of violations of such sections, and each such person shall be deemed to have performed acts equivalent to and constituting an appointment by such person of the superintendent to be his true and lawful attorney upon whom may be served all lawful process in any action, suit or proceeding arising out of a violation of such sections. Copies of all such lawful process shall be served on the superintendent and transmitted by registered or certified mail by the superintendent to such person at his address last of record with the superintendent. Service of process fee shall be paid at time of service on the superintendent in amount specified in Section 101 [59A-6-1 NMSA 1978] (fee schedule) of the Insurance Code.
NMS § 59A-37-10