New Mexico Statutes 1-2-6. Election board; appointment
A. The county clerk on or before forty-two days next preceding a statewide election shall appoint the necessary election boards for that election, and before twenty-one days next preceding a special election the county clerk shall appoint the necessary election boards for that election. The appointment of the members of each election board shall be in writing and delivered to the person receiving the appointment.
B. The county clerk shall maintain in a public place in the county clerk’s office a list of the members of the election board, the positions of the election board members and the assignments of the election board members. The list shall be made available at least forty days before a statewide election and at least twenty days before a special election and shall be updated when changed until forty-five days after adjournment of the state or county canvassing board or until forty-five days following any recount, contest or other judicial inquiry, whichever is later.