No state regulation concerning hybrids found.
Dona Ana County requires a permit to own a hybrid animal: https://donaanacounty.org/sites/default/files/pages/266-2013.pdf#overlay-context=animal (134-16.J)
The city of Las Cruces prohibits wolf hybrids. Their stance on feline hybrids is not specified as with the wolf hybird, however it does state that any member of the felidae family is prohibited except felis catus: https://library.municode.com/index.aspx?clientId=11136 (Article 1, Sec. 7.1, 1-11) Anectodally, in 2014 a Savannah owner was told by Animal Control that F5 or later feline hybrids are not prohibited, however NO municiple code could be found to support this.
Disclaimer: Please check all local, city, county, township, homeowners’ ordinances in your area first before acquiring any hybrid or exotic animals.