In CT you'll typically only find small (relative to Arizona) pieces of public land. But there are some beautiful parts of the state. I'm really only familiar with the southwest corner.
The HAZ MapDEX
can help get you started. You'll likely need to research elsewhere for details though.
Look for Sessions Woods (Nassahegon), Ragged Mountain, Talcott Mountain, and Penwood State Park nearby.
I have relatives up north in East Hartland near the Mass border. Check the Tunxis State Forest and spots around the huge Barkhamsted Reservoir for hikes in that area if you don't mind driving a little farther.
Here's a link to state park and state forest maps in CT:
http://www.ct.gov/deep/cwp/view.asp?a=2 ... v_GID=1650
edit: the mapDEX link is only on Hartford area hikes right now. Change to All Regions for more hikes. CT is a small state. HAZ regions in AZ are larger than all of CT! Perspective!