NEVER go near a wild animal!
You risk exposure to many diseases, even if you do not notice any symptoms.
For the health of other wild animals and humans alike, PLEASE report animals behaving suspiciously to your local police or animal control officer. Never attempt to feed, pet, or handle wild animals or even strays.
To discourage wildlife from living in or around your home, cap chimneys, screen crawl spaces, and repair openings into buildings. This also includes securing potential food sources (garbage cans, pet or livestock food, and even birdseed). Contact the Wildlife Division at 860-424-3011, or a Nuisance Wildlife Control Operator, for information on wild animal behavior and control techniques.
It would also be wise to take advantage of any vaccinations available to your domesticated animals. Most of these diseases will affect your pets (and perhaps you). Many diseases are simply more deadly in the wild due to lack of veterinary care - occasionally, sick animals can even be saved if brought in in time. Be smart with your own care!
Below is a pdf of Connecticut's reportable diseases. I did not describe all of these in this website, as some are not currently threats in the area or information is limited, but educating yourself is important!