FEDERAL RULES APPLYING TO CERTIFYING ELECTION
States certify election results, often the governor has to sign off. States have to follow their state laws relating to contested election results that were on the books prior to the election. They can't change the rules after the fact.
Congressional Research Service
The Electoral College: A 2020 Presidential Election Timeline
https://crsreports.congress.gov/product/pdf/IF/IF11641
EXCERPTS:
November 4-December 14, 2020: Counting Popular Votes and Filing Certificates of Ascertainment
Following election day, the states are to count and certify popular vote results according to their respective statutory and procedural requirements. When the states have completed their vote counts and ascertained the official results, the U.S. Code (3 U.S.C. §6) requires the state governors to prepare, “as soon as practicable,” documents known as Certificates of Ascertainment of the vote. The certificates must list the names of the electors chosen by the voters and the number of votes received in the popular election results, also the names of all losing candidates for elector, and the number of votes they received. Certificates of Ascertainment, which are often signed by state governors, must carry the seal of the state….
December 8, 2020: The “Safe Harbor” Deadline
The U.S. Code (3 U.S.C. §5) provides that if election results are contested in any state, and if the state, prior to election day, has enacted procedures to settle controversies or contests over electors and electoral votes, and if these procedures have been applied, and the results have been determined six days before the electors’ meetings, then these results are considered to be conclusive, and will apply in the counting of the electoral votes………..
Joint Session Challenges to Electoral Vote Returns
While the tellers announce the results, Members may object
to the returns from any individual state as they are
announced………………An objection to a state’s electoral
vote must be approved by both houses in order for any
contested votes to be excluded
==In NM, the contested part starts after the state certifies.
NMSA 1-14-1, 1-14-2 AND 1-14-3.==