New Mexico Statutes Chapter 22. Public Schools § 22-5-9. Local school board vacancies

A. A vacancy occurring in the membership of a local school board shall be filled at an open meeting, at which a quorum of the membership is present, by a majority vote of the remaining members appointing a qualified elector to fill the vacancy.

B. A qualified elector appointed to fill a vacancy occurring in the membership of a local school board shall hold that office until the next regular school district election when an election shall be held to fill the vacancy for the unexpired term.

C. If a qualified elector is not appointed to fill the vacancy within forty-five days from the date the vacancy occurred, the department shall appoint a qualified elector to fill the vacancy until the next regular school district election.

D. In the event vacancies occur in a majority of the full membership of a local school board, the department shall appoint qualified electors to fill the vacancies. Those persons appointed shall hold office until the next regular school district election when an election shall be held to fill the vacancies for the unexpired terms.