In my state (Maryland) there are two categories of private school. With one, there is at least some state supervision, teachers have to be certified, etc. The State Board of Education must approve these schools. A few of the private schools are in this category.

The other category is called "church exempt." Quite simply these are exempt from education regulations. They only need to show that they are operated by a church organization. A large number of the schools are in this category.