The co-pilot was flying the Beech 100 aircraft on the return trip from Toronto. This was the Co-pilot’s first flight on the King Air 100. The crew reported that the aircraft touched down on the runway on the wheels, but continued to settle. The propellers then struck the runway and the aircraft skidded to a stop on the fuselage. The two pilots and two passengers exited the aircraft without any injuries. Tracks in the freshly fallen snow indicated that the landing gear was initially extended and that the aircraft touched down first on the left main landing gear. Neither pilot could recall selecting the landing gear down or ascertaining the position of the landing gear. It was reported that the landing gear position selector handle was in the “down” position after the occurrence. Damage to the aircraft and an examination of the landing gear extension/retraction mechanism revealed that the landing gear was retracted fully when the aircraft was on the runway but that it had subsequently started to extend. No malfunctions were discovered with the landing gear position selector handle, the landing gear warning system or the landing gear.