Amusante, if you're in CT, the short answer is -- no, you can't do that.
From the
Hunting Laws and Regulations page of the DEEP website:
Trap or target shooting on any state property or public hunting area is prohibited unless the area is a designated shooting range.
There are four state owned public shooting ranges available for target shooting, patterning shotguns and sighting in rifles.
So unless you can get permission from a private landowner to shoot on his property, you'd be be breaking the law, license or no license.
That website is your best resource for answering such questions, or for finding out whom to ask.