Not much around New England and nothing really close to CT.
Aside from New England dragway in Epping, New Hampshire (long drive) you have Englishtown/Raceway Park in New Jersey; a great track but also a long drive..I know, I've been there many times.
Check the link for more info.
http://63.222.245.176/etown/
With the absurd lack of drag tracks in the area, no wonder people street race.
A six-hour round trip drive to get to a track is not my idea of time well spent but if you want to race legally and get a real et record, I suggest Englishtown or Epping.