Gmil,
An out of state license is $100.00. You only have to bring them to the check in station during the gun season. The rest of the time you just fill out and mail a "kill card" to report the harvest. You do have to take a bowhunting safety course before you can get the license. You can take it in Mass or CT and they are free. One other thing to mention is that Connecticut is a state that requires written permission to hunt private land. More info can be found at their web site:

http://www.ct.gov/dep/cwp/view.asp?a=2700&q=323414&depNav_GID=1633

Bob