We live south of you in MA. This is my second year un/homeschooling. With our 2e/pg ds8, I was told by an expert a couple of years ago that I would have to un/homeschool too. We were in similar shoes to you with our son when he was in kindy.
I keep a log of reading, math, science, history, etc. developments for myself on a wiki, which I do not give to local school districts. That's for my own personal sanity and reduce my anxiety. In MA, I don't have to provide a reading log or any of this detailed information to local officials. I've found it very helpful, in particular, to keep a log of reading material because you can spot the acceleration jumps and points where the interest changes. I can also see if there's any big gaping holes.
My advice is to stick what you are legally obligated to report and not give them an inch more. For the purposes of reporting to local officials, give them information that's grade level or slightly above - not more, imo. This is not the time or place to be an overachiever or overenthusiastic with reporting, imo. You can make a rod for your own back if you do - or that's what other mothers here in MA have found out.
In NH, it's my understanding that you need to submit a reading log -
http://nhhomeschooling.org/law. The reading log only has to be a page or two long. Well, there's a lot of gray then with what books you report and disclose. NH (and MA) are really only interested in making sure that the child is progressing in their education. Again, though, there's a lot of gray with what they consider 'progress' or what you reveal to a local officials.
In MA, the annual progress report can be quite minimal in comparison -
http://www.ahem.info/ProgressReportA.html. 
