It is legal to marry your cousin in New Mexico. State law does not prohibit marriage between first cousins or more distant cousins. In fact, New Mexico specifically allows first cousins to marry, and there are no special restrictions or requirements for such marriages.
The only relationships prohibited by New Mexico law are those between closer relatives, such as siblings, half-siblings, parents and children, or uncles/aunts and nieces/nephews.
When applying for a marriage license in New Mexico, you do not need to declare your cousin relationship on the application, although a county clerk may ask if you are related. This does not prevent first cousins from marrying, as the law does not consider this an impediment.
Marrying your first cousin is fully legal in New Mexico, and there are no legal barriers or additional requirements for cousins wishing to marry in the state.
Sources
[1] https://local.newsbreak.com/news/4053576471482-is-it-illegal-to-marry-your-cousin-in-new-mexico-here-s-what-the-law-says
[2] https://www.findlaw.com/state/new-mexico-law/new-mexico-annulment-and-prohibited-marriage-laws.html
[3] https://dataminingdna.com/can-first-cousins-marry-in-new-mexico/
[4] https://en.wikipedia.org/wiki/Cousin_marriage_law_in_the_United_States
[5] https://www.legalmatch.com/law-library/article/cousin-marriage-laws.html
