N.M. Stat. § 39-6-1
Whenever it shall be necessary to levy any writ of attachment, replevin or execution under the laws of this state upon any livestock or herd of cattle that are ranging at large with other livestock or cattle over any range country, and when it would be impossible or impracticable to round up, gather or take possession of the same under such process without, at the same time, rounding up and cutting out the livestock belonging to other owners, then and in such case, the sheriff or other officer holding such writ, shall only take possession of such stock as he may be able to get without interfering with the livestock of other owners, and as to the balance, it shall be sufficient, in order to subject them to the lien of said writ, that the officer shall file with the county clerk of the county in which the brand of such livestock is recorded, a certified copy of said writ, and immediately upon the filing thereof the county clerk shall note the same in the reception book of his office, and shall also note the same in red ink on the margin of the page of the book where such brand is recorded, and shall properly index the process in the general and other proper indices of his office: provided, that if said livestock range is in more than one county, then the officer may file a like certified copy of the writ and brand in any such county, and the same shall have like binding effect as a lien upon such livestock.
NMS § 39-6-1