On August 17, 2020, about 2236 eastern daylight time, a Piper PA-34-200, N41382, was substantially damaged when it impacted a house near the Groton-New London Airport (GON), Groton, Connecticut. The flight instructor and pilot receiving instruction sustained minor injuries. An occupant of the house was not injured. The airplane was operated as a Title 14 Code of Federal Regulations Part 91 instructional flight. According to the flight instructor, they departed GON about 1700 hours and flew direct to Bangor International Airport (BGR), Bangor, Maine, where they landed uneventfully, and the fuel tanks were filled. According to the flight instructor, the flight departed BGR around 2000 then proceeded to Augusta State Airport (AUG), Augusta Maine, (where the pilot receiving instruction performed one touch-and-go landing) then to Portland International Jetport (PWM), Portland, Maine (where the pilot receiving instruction performed three touch-and-go landings). After the last touch-and-go landing, the flight proceeded to GON where the pilot receiving instruction performed two touch-and-go landings to runway 23. The flight departed and remained in the traffic pattern for the same runway, where, when abeam the approach end of runway 23 with the landing gear extended and 10° of flaps extended, the pilot receiving instruction began to descend while turning onto the base leg of the airport traffic pattern. The flight instructor stated that at the time he heard an engine sputter and verified the controls were in the proper position. He heard the engine sputter again, "felt the [airplane] jerk," and took control of the airplane. He maintained airspeed and verified the engine controls were full forward. He retracted the flaps but decided to leave the landing gear extended due to the altitude and proximity to the airport. He verified the malfunction to be the right engine and felt it was developing some power but with less output than the left. He briefly pitched nose down, then nose up, and when he noticed a high descent rate, he moved the right propeller control to the feather position and placed the right mixture control to idle cutoff. He looked for a place to land and maneuvered for landing on a street. While flaring to land, he felt a collision. The airplane came to rest suspended by the roof structure of a house. Examination of the cockpit while the airplane was suspended on the roof was not performed by an Federal Aviation Administration inspector for safety concerns. A photograph of the throttle quadrant taken before the airplane was removed from the house revealed the left throttle control was full forward and the right throttle control was at the aft stop. The left propeller control was about 65% forward travel and the right propeller control was 75% forward travel. The left mixture control was about 60% forward travel, while the right mixture control was at idle cutoff. The left cowl flap was closed while the right cowl flap was open. The left engine alternate air control was on, while the right engine alternate air control was off. The airplane was recovered for further examination of the airframe, engines and their systems, propellers and propeller governors. Following removal from the house, the FAA inspector reported fuel was present at both fuel strainers and oil was present in each engine. Examination of the airplane following recovery revealed all engine controls for both engines remained attached to their respective attach points at each servo fuel injector and propeller governor. Flight control continuity for the ailerons, elevator, and rudder was confirmed except where the control cables were cut for recovery. The flap handle was in the down/stowed position, consistent with the flaps being retracted. Both auxiliary fuel pump switches were in the on position, and both electrically tested satisfactory. Both fuel tanks of both wings were breached and did not contain any fuel, and neither fuel strainer contained any residual fuel. The left fuel selector was in the ON position and the right fuel selector was in the CROSSFEED position. No obstructions of the fuel supply lines were noted. Both CROSSFEED drains were checked and about 6 ounces of fuel drained from the bottom of the airframe. The fuel odor and viscosity were consistent with 100LL, but the liquid was cloudy and was not tinted blue. Testing detected no water in the fuel sample. Operational testing of each fuel selector revealed no evidence of preimpact failure or malfunction. Examination of the left and right engines and their systems revealed no evidence of preimpact failure or malfunction. Both propeller governors and propellers were examined at the manufacturer’s facility with virtual oversight provided by the National Transportation Safety Board. Examination of the left propeller revealed impact damage that precluded functional testing. Disassembly of the propeller revealed no evidence of preimpact failure or malfunction. The damage to the propeller blades was consistent with the engine not developing high power at impact. Visual examination of the right propeller revealed the blades appeared to be on the start locks. Although the amount of engine oil drained from the right cylinder was not quantified, it was greater than the amount if the propeller was in the feathered position. This was consistent with the propeller blades being in low pitch and that the governor had not dumped the oil to the engine. Following removal of the start lock/feather stop sleeve assembly and when air pressure was removed, both blades moved to the feather position. Cycling of the propeller blades from feather to low pitch was performed several times using shop air with no discrepancies noted. No evidence of preimpact failure or malfunction was noted to the propeller, and the blades exhibited minimal damage consistent with the engine not developing power at impact. The right propeller was not disassembled. Operational testing of the left propeller governor revealed several minor out-of-tolerance conditions (such as control lever travel, high rpm setting 40 rpm too low, and relief pressure 1 psi too high). All other checks, including feather check, were within limits. Operational testing of the right propeller governor revealed all checks, including feather check, were within limits. Only one setting (high rpm setting) was 21 rpm too low. Neither propeller governor was disassembled.