Have you looked up therapy groups on the internet? I'm sure the criteria for each is different, and every state and every institution may have different rules.
I have taken mine to nursing homes, day cares, Fairs, and Head Start. I have no certification; we just call for an appointment, or sometimes just show up! We have interacted with retarded adults and autistic children.
I don't do nursing homes anymore, however, because many residents do not like having an animal in their "house". You might arrange for an outdoor visit, perhaps on their patio. Then you wouldn't offend the picky ones.
I know the Oklahoma Children's Hospital allows horses. There is such a wide variety of statutes and criteria. You could try contacting your Department of Human Services. Or call the operator at your state Capital and see if she can direct you to the proper Department.