N.M. Stat. § 49-9-5
The individual, company or corporation filing said protest shall be required to follow the same with a proper proceeding in law or in equity, instituted in the proper district court of said county in which said city is located, against the said party or parties applying for said deed or deeds to said land to test the question as to who is the owner of said land and entitled to the deed therefor from said trustees: provided, that if said protest shall be filed by said citizens on behalf of said city as aforesaid, then said city and trustees shall institute and prosecute said suit in the name and on behalf of and at the expense of said city. Said suit or proceeding shall be instituted by the party filing said protest within twenty days of the filing of said protest: provided, that if the party filing said protest is in possession of said land then the adverse party shall institute said suit within said time, and the city council and trustees of said city shall withhold the execution and delivery of any deed to either of said parties for any portion of said land so in controversy until such controversy shall be settled and the court shall determine as to who is rightfully entitled to the deed therefor from said city or town: provided, that parties to such controversy shall have the right to amicably adjust said controversy as to such land and upon such adjustment shall file a statement thereof with the city clerk, and upon such statement being filed the city council and trustees shall cause to be executed deed or deeds to the parties as may be agreed upon between them and shown in such adjustment so filed.
NMS § 49-9-5