N.M. Stat. § 4-41-10
All sheriffs shall at all times be considered as in the discharge of their duties and be allowed to carry arms on their persons. On the appointment of any regular or permanent deputy sheriff, it shall be the duty of the sheriff to file one notice of the appointment in the office of the county clerk of the sheriff's county and one notice of the appointment in the office of the clerk of the district court of that county, and each of the sheriff's deputies shall file an oath of office in the office of the county clerk. Any sheriff is hereby authorized at any time to appoint respectable and orderly persons as special deputies to serve any particular order, writ or process or when in the opinion of any sheriff the appointment of special deputies is necessary and required for the purpose of preserving the peace, and it shall not be necessary to give or file any notice of such special appointment; however, the provision authorizing the carrying of concealed arms shall not apply to such persons. Provided, no person shall be eligible to appointment as a deputy sheriff unless the person is a citizen of the United States of America. There shall be no additional fees or per diem paid by the counties for any additional deputies other than as provided by law.
NMS § 4-41-10