On March 31, 2019, about 1630 Pacific daylight time, a Cessna 172L, N7033Q, was substantially damaged when it was involved in an accident near Placerville, California. The pilot was not injured. The airplane was operated under the provisions of Title 14 Code of Federal Regulations Part 91 as a personal flight. The pilot reported that after departing the traffic pattern, the engine began to run rough. He checked the throttle position, mixture control, fuel tank selection, and engine oil pressure. He then turned on the carburetor heat and the roughness increased without an increase in engine speed. The airplane was about 1,500 to 2,000 ft above ground level (agl) and the pilot decided to return to the airport for landing. The airplane was not able to maintain altitude and landed in trees about 300 ft short of the approach end of runway 23. Postaccident examination revealed that both fuel tanks and the gascolator were full of fuel, and all fuel lines were secure and unobstructed. The engine air inlet filter was free of debris, and all the internal passages of the filter box and carburetor heat ducting were clear. The engine contained 7 quarts of oil (maximum 8) and there was no evidence of catastrophic engine failure. The propeller blades along with the engine and its ancillary components did not appear to sustain any evidence of impact damage. The inner surface of the exhaust pipe appeared coated in black soot, and similar sooting was present on the electrodes of all spark plugs. The data tag for the carburetor had partially worn away such that the manufacturer could not be determined, although it appeared to be of the Marvel-Schebler type, with a part number of 4SPA and serial number 10-3678-12. Further examination revealed evidence of a fuel leak at the body-to-bowl join, and all four bowl securing screws were loose. The bowl was loose and could be moved by hand, and disassembly revealed fretting and polishing on the bowl and body join surfaces. The accelerator pump plunger assembly shaft appeared loose, and both its packing and washer had detached from the carburetor body and were floating freely on the shaft. Further disassembly revealed that the carburetor was equipped with a brass-type float and the float level (distance between the top of the float and the body-to-bowl join) was 3/32 inch rather than the required 7/32 inch. The float was intact and did not leak when tested in a bowl of fuel. During disassembly Teflon-tape pipe sealing material was present on the threads of the carburetor inlet fuel fitting. Maintenance records indicated that the engine was last overhauled in January 2000, about 1,587.8 flight hours prior to the accident. The records did not indicate that the carburetor had been overhauled at that time, and there were no entries indicating any work had been performed on the carburetor over the next 19 years until the accident. The last documented maintenance event performed on the engine was for an annual inspection and occurred on November 13, 2018, 37.8 flight hours prior to the accident. The 4SPA carburetor was the subject of a series of service bulletins (SBs): MSA-3, issued by Precision Airmotive Corporation in 1991, established a 10-year overhaul period for the carburetor. SB-17 issued by Marvel-Schebler Aircraft Carburetors, LLC., dated August 12, 2010, with a subject of, "Body to Bowl Fuel Leaks", directed an inspection of the carburetor every 100 hours of engine operation. The SB described reports of loose body-to-bowl joints, with resulting leakage past the body-to-bowl gasket. Compliance required a visual inspection of the carburetor for evidence of movement, with remedial repairs should such evidence be found. Lycoming mandatory SB 366C, dated June 2, 2016, also directed a similar inspection of the carburetor every 50 hours of engine operation. The pilot stated that he had about 1 hour of flight experience in the accident airplane and that when operating other Cessna 172s, the engine speed would usually drop during the carburetor heat check by between 100 and 200 rpm. He stated that the rpm drop for the accident airplane was about 400 rpm. The pilot provided documentation from the airplane's owner who stated that he was aware that pilots had experienced a similar rpm drop but that the airplane had been examined and no anomalies were discovered. The owner's recommendation was to lean the fuel/air mixture when necessary. The before takeoff checklist in the Cessna 172L Owner's Manual includes a carburetor heat check. It does not specify an appropriate rpm drop but instead simply requires that the pilot, "check operation".