N.M. Stat. § 73-11-43
If a purchaser does not pay the amount of his bid before ten o'clock of the day succeeding the sale, the property shall be reoffered for sale and the bid of any person refusing to make any such payment shall not be received on the resale of any such property. After receiving the amount for which said real estate shall be sold, the assessor-collector shall execute and deliver to the purchaser thereof a certificate of sale containing a description of the property sold, and stating the name of the person or persons against whom the same was assessed, or that the same was assessed against unknown owners, as the case may be, the amount paid therefor, that it was sold for taxes, the amount and for the year or years for which the taxes were assessed, the amount of interest, penalties and costs, the date of sale, and the consideration or amount so paid therefor at such sale, that the assessor-collector by virtue of the authority vested in him by law, has sold and does convey said real estate to said purchaser, his heirs and assigns, subject to the right of the owner to redeem the same within three years from date of sale by paying to the purchaser, his heirs or assigns, the amount paid therefor at such sale with interest thereon at the rate of one and one-half percent per month from date of sale. Such certificate must be recorded in the office of the county clerk of the county in which such real estate is located in a book to be kept for the purpose of recording such certificates and when so recorded, shall vest in the purchaser, his heirs or assigns, a complete legal title to the real estate described therein, subject however, to redemption as herein provided, and such property shall thereafter, unless redeemed, be assessed in the name of the purchaser, or his assigns, but the former owner shall have the right to redeem the same at any time within three years from the date of sale by paying to the assessor-collector then in office, for the use of the purchaser the amount of purchase money with interest at the rate of one and one-half percent per month from date of such sale, together with any taxes that may have been paid upon such real estate by the purchaser and assignees with interest thereon at the same rate; and such former owner may retain possession of said real estate until redeemed, or until the time of redemption has expired.
The assessor-collector shall keep a book of sale containing the dates of sale, description of the property sold, name of purchaser and amount for which sold. Upon the redemption of any property sold, as herein provided, the assessor-collector shall enter the fact of such redemption upon his book of sales, and shall issue to the person redeeming a certificate of redemption describing the property and giving the date of redemption and amount paid, upon the production of such certificate of redemption the county clerk shall mark the word "redeemed" with the date of redemption and by whom redeemed, on the margin of the page where the record of such certificate of sale is made, and from the date of such redemption when so made, and noted, the certificate of sale shall be deemed canceled and annulled.
NMS § 73-11-43