I don't know the specifics so the best thing to do is call your county and ask. You generally can apply for mother in law or grandma suite.

Every county or city in the U.S. has it's own rules that govern basement kitchens. Some counties will allow it, but you must promise not to rent it as a second dwelling. The county will even go so far as to place a restriction in your deed. So if and when you sell, the prospective buyers will be bound by the restrictions also.

In other places where it is legal, you have to apply for a permit.

Tom