THE INSTRUMENT RATED PRIVATE PILOT HAD FLOWN IN IMC CONDITIONS ON TWO IFR FLIGHT PLANS THROUGHOUT THE DAY FROM MIAMI, FLORIDA TO GROTON, CONNECTICUT. HE HAD UPDATED HIS DESTINATION AND ALTERNATE WEATHER WHILE EN ROUTE AND KNEW OF THE CONTINUING CONDITIONS. AFTER REPORTING BABET INTERSECTION AND RECEIVING CLEARANCE FOR THE APPROACH TO LAND FOR RUNWAY 23, THE PILOT DESCENDED THE AIRPLANE TO APPROXIMATELY 680 FEET MSL AND ENGAGED THE AUTOPILOT. THE AIRPLANE DESCENDED SLOWLY BELOW THE MINIMUM DESCENT ALTITUDE AND IMPACTED A WOODED AREA APPROXIMATELY 1.5 MILES FROM THE AIRPORT. THE PILOT WAS VISUALLY SCANNING OUT THE AIRPLANE'S WINDOW AND DID NOT NOTE THE DESCENT BEFORE IMPACT. HE REPORTED NO FAILURES TO ANY AIRPLANE SYSTEM OR RADIOS. THE FAA COORDINATOR FOUND NOTHING UNUSUAL WITH THE AIRPLANE AND DID STATE THAT THE PILOT REPORTED BEING TIRED AT THE TIME OF THE APPROACH. THE MINIMUM DESCENT ALTITUDE WAS 660 FEET.