My guess is that CT state parks are closed for the season at
this time. I would think you could stealth camp a night anyway
without much hassle. If you're coming up I95 you can make
a short detour to "SLeeping giant" state park. This one
doesn't normally have organized camp sites, but it looks as though
one could sleep in comfort off one of the less traveled roads.

When exiting off Rt 10, skip the most obvious parking lot area.
Take the next left, which winds up a hill. There are a couple of
trailheads along the road with good pull offs for parking.
For a nice morning hike before you're off to Cape Cod, walk
the blue trail. Takes you to a number of good overlooks on
the nearby hills.

/m