N.M. Stat. § 10-2-12
It shall be the duty of the board of county commissioners of each county at each regular meeting thereof on the first day of each meeting to examine and inquire into the sufficiency of all the official bonds given or to be given by any county or precinct officer as required by law, and if it shall appear that any one or more of the securities on the official bond of any county officer has or have removed from the county, died, or become insolvent, or of doubtful solvency, the said board of county commissioners shall cause such county or precinct officer to be summoned to appear before the said board on a day to be named in said summons, to show cause why he should not be required to give a new bond with sufficient security, and if at the appointed time he shall fail to satisfy said board as to the sufficiency of the present security, an order shall be entered of record by said board requiring such county or precinct officer, to file in the office of the county clerk within twenty days, a new bond to be approved as required by law, unless the number and pecuniary ability of other securities on said bond shall be such as to satisfy the board that the bond is sufficient, notwithstanding one or more of the securities on said bond may have removed, be dead, insolvent or of doubtful solvency, in which case the bond in question may be, in the discretion of the board, held sufficient. In the event any such bond is found insufficient, and a new bond is not filed as ordered, the fact shall be certified by the board of county commissioners to the district court of the county, and shall also be certified to the district attorney of the judicial district wherein such county is located; and it shall thereupon become the duty of the district attorney to cause a hearing to be had in said district court for the purpose of adjudicating and declaring a vacancy in such office, in the event the district court determines, after a hearing, that the bond is in fact insufficient, and such officer fails within five days after the district court has so found to file a new bond with sufficient surety as required by law. Upon the entry of such decree of vacancy it shall thereupon become the duty of the appointing power to fill such office in the manner provided by law.
NMS § 10-2-12