NO, you can't shoot it if it's in a tree.

From the regulation:

(c) Method of take
(1) No person shall hunt, pursue, kill, take or attempt to take any wild turkey without a validated turkey permit, in addition to the license required by Section 26-27 of the General Statutes.
(2) No animal, including a dog, may be used in hunting or pursuing any wild turkey.
(3) No person shall take or attempt to take any wild turkey with the aid of real or artificial bait; over any baited area; with the use of electronic amplified turkey calling device or live decoy.
(4) No person shall take or attempt to take any wild turkey by participating in a cooperative drive or assist in hunting, pursuing or killing of wild turkeys without a validated permit. This provision shall not prohibit a hunter that has voided his or her turkey permit due to the use of all the harvest tags attached to the permit, from calling for another hunter with a valid turkey permit.
(5) It shall be unlawful to shoot from a building or other permanent structure.
(6) No person shall take or attempt to take any wild turkey which is roosted in a tree.