On April 25, 2020, about 1340 eastern daylight time, a Piper PA-28-151, N33005 was substantially damaged when it was involved in an accident near East Hampton, New York. The pilot and two passengers were not injured. The airplane was operated as a Title 14 Code of Federal Regulations Part 91 personal flight. According to the pilot, they departed Igor I. Sikorsky Memorial Airport (BDR), Bridgeport, Connecticut about 1045. She landed at East Hampton Airport (HTO) about 1115 and parked the airplane. She subsequently returned to the airplane with the passengers about 1315. The pilot then reviewed the weather and performed a preflight inspection of the airplane with no anomalies noted. The pilot started the engine and taxied to the delta intersection of runway 28, where she performed an engine run-up procedure and configured the airplane for takeoff. The takeoff roll was normal, but after rotation during the climb, the pilot noticed a vibration and diminished engine power, though the throttle was in the full throttle position. At 400 or 500 feet mean seal level (msl), the engine began sputtering. The pilot made a successful right turn back to the airport before the engine lost power completely. The pilot was able to return to the airport and land about 3/4 down an available runway. The airplane went off the end of the runway through a deer fence and came to rest in a field. Examination of the airplane by a Federal Aviation Administration (FAA) inspector revealed substantial damage to both wings and the fuselage. The propeller displayed scratches on the leading edges of both blades with no curling of the blade tips. No visible damage was present in the engine compartment. No oil or fuel leaks were noted. Engine oil on the dipstick showed the correct level and appeared clean. Examination of the throttle, mixture, and carburetor heat controls revealed that they were intact, displayed correct movement, with no evidence of binding. The fuel in the left- and right-wing fuel tanks was sampled, and no debris or water contamination was visible. Examination of the fuel strainer showed no debris or water, and fuel was present in both wing tanks with the fuel quantities at a level just below the tabs. The drive train was rotated by turning the propeller and compression was evident on all four cylinders. After the examination, the fuel selector was turned on, the engine was primed using the electric fuel pump and started. The engine was first idled at 1,200 rpm, and then power was increased to 1,500 rpm. The engine ran normally, and no vibrations or sputtering was noted. After 8 minutes, the engine was shut down. Review of the meteorological conditions that existed around the time of the accident and the carburetor icing chart from FAA Special Airworthiness Information Bulletin CE-09-35 “Carburetor Icing Prevention” indicated a potential for icing at glide (idle) power and cruise power at the temperature and dew point that existed around the time of the accident. Review of the pilot’s NTSB Form 6120.1 Pilot/Operator Aircraft Accident/Incident Report revealed that after the runup, the pilot had turned the “Carb heat off”, and examination of a post-accident photo of the instrument panel also indicated that the carburetor heat control was in the off or nearly off position. The Emergency Procedures section under Engine Roughness in the Cherokee Warrior pilot operating handbook (POH) described engine roughness as usually due to carburetor icing, which is indicated by a drop in rpm and may be accompanied by a slight loss of airspeed or altitude. It went on to advise that if too much ice is allowed to accumulate, restoration of full power may not be possible; therefore, prompt action is required. It further advised, in part, that once the carburetor heat is selected on, the rpm will decrease slightly, and roughness will increase. Pilot should wait for a decrease in engine roughness or an increase in rpm, indicating ice removal. Further review of the POH revealed that the Engine Power Loss During Takeoff and Engine Power Loss in Flight sections also advised to turn on the carburetor heat.