N.M. Stat. § 4-34-3
Should a majority of the votes at such election be cast in favor of the place named in the petition, the county seat shall be removed to that place, and it shall be the duty of the board of county commissioners, as soon as the citizens of that place have delivered the deed and paid over the sum of money mentioned in the written guaranty provided for in Section 4-34-1 NMSA 1978, to cause to be erected upon the site so provided a courthouse and jail to cost not to exceed three times the amount paid by the citizens, including said amount.
For the purpose of such construction, the board of county commissioners is hereby authorized to issue bonds of that county in such form as the board of county commissioners shall determine, for such time and bearing such rate of interest as it may deem best, such bonds to be sold at, above or below par as permitted by the Public Securities Act [6-14-1 to 6-14-3 NMSA 1978], or taken at par in payment for such construction. The contract for the construction of such buildings shall be let to the lowest responsible bidder after advertising the time and place of opening sealed bids for the same in a newspaper published in the county once a week for four consecutive weeks, such contractor to furnish a good and sufficient bond for the completion of such buildings according to the plans and specifications.
NMS § 4-34-3