CE-680A First Officer reported uncommanded aircraft movement on a ramp area when parked on an an area of ice at night; after releasing the parking brake. The crew set the brakes to stop the movement; no damage occurred; then repositioned the aircraft to another area on the ramp.

Narrative

Arrived at Flight Level FBO located at ZZZ at night. Upon arrival; the FBO Marshaller had marshalled the crew to park next to the middle row of hangars located south of the FBO building. After the shutdown without APU checklist was completed (minus the battery switches being placed into OFF due to the 30 second requirement after shutdown); the marshaller gave the instruction to the crew that the aircraft was chocked. The PIC elected to release the parking brake and upon release; the aircraft began to roll back. Both PIC and SIC reached for the auxiliary hydraulic pump to turn it on and then placed pressure on the brakes. The PIC placed the parking brake on. After exiting the aircraft; the SIC found that the aircraft was parked on black ice and on a slight incline which was hard to see from the cockpit. When the parking brake was released; the weight of the aircraft pushed the chocks across the ice until the brakes were re-applied. After discussing other parking options; it was decided to relocate the aircraft under its own power to Flight Level's overflow parking located on the east side of taxiway 1. After relocation; crew spoke with the marshaller who advised that this was their first winter working the line and that the spot they were initially standing on to marshall the crew in was dry; but that they did not survey the area that the aircraft would be parked on. There were no NOTAMs at the airport for ground icing conditions or contaminated ramp areas.Suggestions: Going forward the crew should check the ramp conditions before releasing the parking brake and even then; the aircraft should be powered up with one crew member seated in the cockpit to allow for placing the parking brake back on in case of a similar event.