Each state has individual requirements for kindergarten. In many cases kindergarten is not required by law yet is provided to all kids if their guardians what them to attend. In fact very few students do not attend kindergarten when they reach the age of 5 or whatever age is appropriate in the individual state.
Based on your question I believe the answer is to check with local school principals or guidance counselors about the requirements for kindergarten in your area. I suspect you'll find the answer to your questions at the local school level.