N.M. Stat. § 4-38-10
Chairman.
A. The county commission shall select a chairman in a manner and for a term
provided by county ordinance.
B. In the absence of a county ordinance providing for the chairman's selection and
term, the county commissioners shall, at the first meeting of each year choose one of
their number chairman, who shall preside at that meeting and all other meetings if
present; but in case of his absence from any meeting, the members present shall
choose one of their number as temporary chairman.