N.M. Stat. § 1-14-14
Recounts; rechecks; application.
A. Whenever any candidate believes that any error or fraud has been committed by any
precinct board in counting or tallying the ballots, in the verification of the votes cast on the voting
machines or in the certifying of the results of any election whereby the results of the election in
the precinct have not been correctly determined, declared or certified, the candidate, within six
days after completion of the canvass by the proper canvassing board, may have a recount of
the ballots, or a recheck of the votes shown on the voting machines, that were cast in the
precinct.
B. All applications for recount or recheck shall be filed with the secretary of state.