New Mexico Statutes Chapter 1. Elections § 1-15-14. United States senator; vacancy

A. Immediately upon there being a vacancy in the office of United States senator, the governor shall make a temporary appointment to fill the vacancy until such time as an election is held to fill the vacancy for the unexpired term.

B. The election to fill the vacancy for the unexpired term shall be held at the next general election occurring not less than thirty days subsequent to the happening of such vacancy.

C. If the vacancy occurs within thirty days next preceding a general election, the person appointed by the governor to fill the vacancy shall hold office until the next general election occurring more than thirty days subsequent to the happening of the vacancy unless the term of office of such senator shall sooner expire.

D. Candidates to fill a vacancy in the office of United States senator for an unexpired term shall be nominated and elected in the same manner as candidates are nominated and elected for the full term.