Alaska laws are probably the easiest. You don't have to do anything. Literally, if you want to homeschool on your own then that's exactly where you are - on your own! You do not have to file a letter of intent.
Because most of the state is not even on the road system many of the village schools are more like a homeschool environment than a state run institution. One room schoolhouses are the norm in many villages.
The school districts have everything available online - testing, tutoring, etc.
Several of these 'school districts' offer enrollment as a homeschool/ charter/umbrella sort of thing. For people who need financial help with homeschool stuff it can be a help, and many people take advantage of that and continue to teach their children whatever they want to although the state will not purchase, reimburse, or recognize christian material as a core material. For instance, I use Five In A Row. I would not be able to purchase this through a program, but I could use it, and I would be able to purchase most, if not all of the books needed through the program. I would simply list it as a 'parent-directed' course.
If you'd rather not do state testing, hand in work samples, or be accountable to anyone outside of your household you don't have to here in Alaska if you're on your own.