N.M. Stat. § 66-5-104
The manner of procuring and serving process in any cause, brought pursuant to the preceding section [66-5-103 NMSA 1978], shall be as follows, to wit:
The plaintiff shall file a verified complaint in one of the district courts of the state, showing a cause of action against the defendant, or his executor, administrator or personal representative, of the class contemplated in Section one (66-5-103 NMSA 1978) hereof; and shall further show in said complaint, or by affidavit, to the satisfaction of the judge of said court, that the defendant, or his executor, administrator or personal representative, is one of the persons contemplated in Section one (66-5-103 NMSA 1978), and the residence of said defendant, or his executor, administrator or personal representative, and a description of the car, or motor vehicle, claimed to have been operated by the said defendant, or his agent, as near as the same can reasonably be ascertained by the plaintiff; and the time, place and nature of such accident, or injury. Upon such showing being made, the judge shall make an order, directing that service of process be made on the defendant, or his executor, administrator or personal representative, as provided in Section one (66-5-103 NMSA 1978) hereof; and, also, that a copy of the process, and complaint, and of said order, and a notice that the same has been served upon the secretary of state, pursuant to this act [66-5-103, 66-5-104 NMSA 1978], be delivered to the defendant personally, or his executor, administrator or personal representative, without the state. Proof of such service shall be made by affidavit filed in said cause, and service shall be deemed complete thirty (30) days from the date such personal service is made on the defendant, or his executor, administrator or personal representative.
The court in which the action is pending shall, upon affidavit submitted upon behalf of the defendant, or his executor, administrator or personal representative, grant such additional time to answer, or continuances, as shall be reasonably necessary to allow defendant, or his executor, administrator or personal representative, full opportunity to plead and prepare for the trial of the said cause.
NMS § 66-5-104