New mexico constitution
Article VI: judicial department
Section 35

Immediately after receiving the commission nominations, the governor may make one request of the commission for submission of additional names, and the commission shall promptly submit such additional names if a majority of the commission finds that additional persons would be qualified and recommends those persons for appointment to the judicial office. The governor shall fill a vacancy or appoint a successor to fill an impending vacancy in the office of justice of the supreme court or judge of the court of appeals within thirty days after receiving final nominations from the commission by appointing one of the persons nominated by the commission for appointment to that office. If the governor fails to make the appointment within that period or from those nominations, the appointment shall be made from those nominations by the chief justice or the acting chief justice of the supreme court. The person appointed shall serve until the first general election following one year after appointment. The appointee's successor shall be chosen at such election and shall hold the office until the expiration of the term in effect at the time of election.