E.S.
That is great that you began home-schooling -you own school.
You can get all the information from the Board of Education in Manhattan. Simply write a letter (do not call- you will not get results). Write a letter (short) stating that you want the rules and regulations about home-schooling in Manhattan. That should give you a start.
Then for any documents or more information . Attend a SCORE meeting at a Manhattan Library. These SCORE meetings or one-to-one FREE business counseling will get you started in your own business with the best advice available.
The Score members are previous business owners or retired individuals who volunteer to help others.
Check out all the licensing bureaus in your state to find out if you need any other papers. There are a million ways to get information. And one of the best ways is to check out the information that the reference librarian has to offer. They usually are up-to-date on the latest rules and regulations and if they are not , they know where to find the information. Visit other small private schools (as a consumer) and see how they are run. (Ask for some documents, information , brochures) . Checking out the competition is a good education.
Any and all of these ways can help you.