It will vary state to state. Here in pa it's the department of health. I'm sure there is an inspection of some kind, but I have never seen it. Our regulations on camps can fit on an index card, and revolve mostly around food service, and septic systems. The ACA accreditation is optional, but also seems quite easy to get so long as your camps practice is commons sense and good judgement.
I use my phone, to type, I work at night, and I'm a bad speller. Pick any reason you want for my misspellings