I believe my state is like others already mentioned-legal to 'say' you are an 'equine dentist', though no licensing or other certification requirements--- but, CANNOT legally administer sedation via injection. I have a friend who several years ago, when a young man had 'hung out his shingle' as an 'equine dentist'(first I'd ever heard of in NM), had him out to do her Fjords. He horrified her by using the same needle to inject both horses, and she resolved to never have him back(and I on hearing her story, resolved never to use him!) I have not heard of him since, and kind of think he 'didn't last' around here.
I have some horses who require sedation, some who don't, so I will stay with my good equine vet, who is both willing and VERY able to do the minis(and others).
Margo