N.M. Stat. § 38-5-14
The court shall permit the parties to a case to express in the record of trial any challenge to a juror for good cause. The court shall rule upon the challenge and may excuse any juror for good cause. Challenges for good cause and peremptory challenges shall be made outside the hearing of the jury. The party making a challenge shall not be announced or disclosed to the jury panel, but each challenge shall be recorded by the clerk and placed in the case file. In civil trials, the opposing parties shall exercise peremptory challenges alternately. In juvenile or criminal cases, the state or prosecution shall pass or accept or make any peremptory challenge as to each juror before the defendant is called upon to pass, accept or exercise a peremptory challenge as to the juror. In civil cases, each party may challenge five jurors peremptorily. When there are two or more parties defendant or parties plaintiff, they shall exercise their peremptory challenges jointly, and if all cannot agree on a challenge desired by one party on a side, then the challenge is forfeited. However, if the relief sought by or against the parties on the same side of a civil case differs, or if their interests are diverse, or if cross-claims are to be tried, the court shall allow each party on that side of the suit five peremptory challenges.
NMS § 38-5-14