§ 1-13-11 NMSA 1978

In the event of a tie vote between any candidates in the election for the same office, the determination as to which of the candidates shall be declared to have been nominated or elected shall be decided by lot. The method of determining by lot shall be agreed upon by a majority of a committee consisting of the tied candidates, the county chairmen of the political parties that participated in the election and the district judge. The county canvassing board shall issue the certificate of nomination or election to the candidate chosen by lot.