N.M. Stat. § 1-12-68
Paper ballots; county canvass; when recount is required.
A. If it appears that defective returns cannot be corrected without a recount of the paper
ballots, the county canvassing board shall immediately notify the district court in writing.
B. The district court shall fix a time and place, which shall be not more than one week after
receipt of notice from the county canvassing board, for a recount of the paper ballots from the
precinct.
C. The county clerk shall immediately notify the county chairs of the political parties that
participated in the election of the time and place of the recount.
D. At the time and place set by the district court, the ballot box shall be opened in the
presence of the district judge or some person designated by the district judge to act for the
district court, the precinct board [election board], the county canvassing board and other
persons desiring to be present.
E. The precinct board [election board] shall then recount the paper ballots and make a new
tally sheet certificate in duplicate to conform to the facts.
F. After the recount is completed, the precinct board [election board] shall replace in the
ballot box the paper ballots and other items taken therefrom and shall lock and return the ballot
box and one key to the county clerk. The other key shall be returned to the district court or its
representative.
G. After being properly corrected, the signature roster and tally sheets shall be disposed of
as in the first instance: one each to the county clerk and one each to the secretary of state.