M.S.
A word of warning- CT is obscenely expensive. Housing is at an ultra premium.
With regards for job searching, I would go to Fortune.com, search for companies headquartered in CT in the Fortune 500 or 1000 range, and then use the sites individually. Fewer major companies are using the job boards because of general scarcity of open roles.
Also, make sure you have a LinkedIn profile with as many connections as you can create. Post that you are considering personal move to CT. LinkedIn also has a jobs area- but primary, headhunters will find you though it.