Following a night landing the pilot taxied to the ramp and was marshaled into a parking space by ground crew personnel. The pilot stopped the twin-engine airplane and set the parking brake before continuing with other checklist items. Unbeknownst to the pilot, the airplane with engines still running began to roll forward until it impacted a tug and ground power unit (GPU), located approximately 25 feet across the ramp. During impact the nose landing gear collapsed and the nose of the airplane came to rest on the rear of the tug. The pilot immediately shut down both engines, and he along with the three passengers exited the airplane unassisted. A Federal Aviation Administration (FAA) inspector examined the airplane and reported that the airplane’s forward fuselage had sustained structural damage during the accident. No anomalies were noted with the airplane's systems.