We lived in CT until my son was 3; I'm never got too into the laws there so I'm not sure how difficult it is to hs there but I know there were very, very few hsers there. At least where we were. I have a friend who hs there now and she's in a group that has members in three counties.
We're in AZ now. Like someone said it is one piece of paper once. You sign saying you will actually teach them english, math, science, etc. The end. There are tons and tons of hsers here (probably because AZ ranks 50th in public schools). The valley itself has tons of unschooler, classical, religious, etc groups - just about anything you can think of. My eldest is extremely social so he just started going to a hs enrichment program at a public school. It's one day a week, free because it's public school, every child there is hs'ed, there is no testing and no academics. It's all the 'enrichment' subjects - art, music, pe, computer, library, etc. Many swimming, gymnastics, karate, art classes are offered here during the day because there are so many hsers.
Personally I think it is more important to have a lot of other hs'ers around than just ease of requirements alone. My kids love that they can go to a park and odds are good there will be other kids there. We take swimming (even my 6 yo), art during the day. Have our choice of about 50 hs support groups. Not every child they know is in school during the day.