N.M. Stat. § 66-5-103
That the acceptance by nonresidents of the rights and privileges conferred by existing laws to operate motor vehicles on the public highways of the state of New Mexico, or the operation by a nonresident, or his authorized chauffeur, or agent, of a motor vehicle on the said highways, other than under said laws, shall be deemed equivalent to an irrevocable appointment by such nonresident, binding upon his executor, administrator or personal representative, of the secretary of state of the state of New Mexico, or his successor in office, to be his true and lawful agent, upon whom may be served all lawful process in any action or proceeding against said nonresident, growing out of any accident or collision in which said motor vehicle may be involved, while same is operated in the state of New Mexico by said nonresident, or by his authorized chauffeur or agent; and said acceptance or operation of said vehicle shall be signification of his agreement that any such process against him, or his executor, administrator or personal representative, which is so served on the secretary of state shall be of the same legal force and validity as if served upon him personally, or his executor, administrator or personal representative, within the state.
NMS § 66-5-103