N.M. Stat. § 13-4-21
That all contracts entered into by the state of New Mexico, any political subdivision of the state of New Mexico or any institution or department of the state of New Mexico, with any person or partnership not a resident of the state of New Mexico, or with any foreign corporation not authorized to do business in the state of New Mexico, for the furnishing of any materials or supplies or for the performance of any public work within the state of New Mexico by such nonresident person, partnership or foreign corporation not authorized to do business in the state of New Mexico, shall contain a specific provision designating an agent of such person, partnership or corporation, resident within the state of New Mexico, with his residence and post-office address, upon whom process and writs in any action or proceeding against any such nonresident person, partnership or corporation may be served in any action arising out of such contract to the same effect as though such person, partnership or corporation were actually and personally served within the state of New Mexico.
NMS § 13-4-21