A fantastic reference to determine the homeschooling laws for each state is Home School Legal Defense Association's website. According to them, it is legal to educate your children at home, in all states. However, the degree of involvement from local educational agencies varies from state to state.
It was very easy to comply with those regulations. We kept our records in a fire proof box, submitted a form annually, and kept our health records current. Those health records were only reviewed once by the Dept. of Health.
Now, we instruct our children under a very favorable homeschooling option that requires us to register under a church-related school and abide by their requirements.
Fortunately, they are very "homeschool friendly" and only require that we submit attendance, mid-year, and final grades for coursework each year.
Their guidelines for high school are more stringent but they also provide official transcripts and senior diplomas. So, it is well worth the extra effort!
Basically, for the high school aged children, we have to submit more detailed information about their course of study. For example, math becomes Algebra 1 or Calculus and science must be listed as Biology or Chemistry.
We also have to inform them when it is time to graduate and allow them time to confirm our plans and develop the transcript.
You are ultimately responsible for teaching your children at home so you need to know and understand the regulations.
Be sure to have a clear picture of the requirements expected of you. Don't count on another person's interpretation of the legal policies pertaining to your rights!