N.M. Stat. § 73-7-19
Where a drainage district has no sufficient outlet within its borders it is hereby provided that said district shall have the right to condemn right-of-way across the necessary lands to reach an outlet, the damages, if any, to the owners of lands through which the right-of-way is procured to be agreed upon by said owner and the commissioners of such district or if they cannot agree upon damages, the said drainage commissioners, shall proceed in the name of such drainage district to condemn such right-of-way which shall be so located so as to do the least damage to private or public property consistent with the proper use and economical construction of such outlet. Such land and right-of-way shall be acquired in the manner provided by law for the condemnation and taking of private property in New Mexico, for railroad, telegraph, telephone and other public uses and purposes.
NMS § 73-7-19