N.M. Stat. § 1-14-18
Recount; recheck; recanvass by canvassing boards.
A. Immediately upon receipt of the certificate of recount or recheck from all the recount
precinct boards [election boards] making a recount or recheck, the proper canvassing board
shall meet and recanvass the returns for the office in question.
B. In making the recanvass, the proper canvassing board shall be bound by the certificates
of recount or recheck from the recount precinct boards [election boards] instead of the original
returns from the precinct boards [election boards].
C. After the recanvass, if it appears that fraud or error has been committed sufficient to
change the winner of the election, then the proper canvassing board shall revoke the certificate
of nomination or election already issued to any person for that office and shall issue a certificate
of nomination or election in favor of the person receiving a plurality of the votes cast at the
election as shown by the recount or recheck, and such certificate shall supersede all others and
entitle the holder to the same rights and privileges as if such certificate had been originally
issued by the canvassing board.