Researching state laws about requirements for homeschooling can be daunting. You could spend hours combing the US Department of Education site to find recent information. So, I hope the following summary and resources will help you save some time.
States vary greatly in their requirements for homeschooling.
Jessica Huseman's ProPublica report "Homeschooling Regulations by State" shows that much of the US requires some sort of notification that a child is being homeschooled, but there are some states that don't have any such requirements. Most states have no requirements on how much education the parents have who are teaching their students at home, and a college degree isn't required in any state. And there are only two states that look at criminal history of parents or other people living in their home.
A majority of states do have certain criteria for the subjects being taught but don't assess what's being taught. Lastly, most states don't require vaccination, and many of the ones that do don't have the records recorded with any authority.
To help you on your quest to find information about your specific state, below are some helpful links, and some have maps with links for individual states.
These links are a quick reference to help identify the basic laws of each state if you're considering homeschooling. Make sure to verify the laws in your state before moving forward, because these laws are subject to change. This can be done by searching homeschool laws on your state Department of Education website or verifying the current laws with an attorney.
If you find any helpful resources for the state you reside in, please comment below with the link to help others.