CE680A First Officer reported failure to properly apply parking brake resulted in momentary loss of aircraft control on the ground.

Narrative

We came in on the ramp in ZZZ went to park did the shut down with APU checklist. I said Parking Brake ON and captain said ON then continued down the checklist and completed it. After the checklist the airplane started rolling back and we still had some pressure in the system for the brakes to work as well as there were chocks behind the wheels thus stopping the airplane without any damage to the airplane or passengers. I am personally unsure if the chocks were already there or not. PIC states that it was the brakes that stopped the airplane but I am not sure if it was the brakes or if it was the chocks or a combination of the two since the PIC advised me that he asked the line personnel if the airplane had stopped on the chocks and they said no. I do remember that after we put the parking brake lever ON at the end the CAS (Crew Alerting System) did come on so it may have been just the parking brake like the PIC said. PIC states he may have turned on the parking brakes then may have turned them back off and he doesn't know why he did that. It was honestly just a blur what exactly happened but this is my best recollection of what did happen but what we do know is we did the checklist but for some reason the parking brake was not actually set at the end of the checklist when I looked back to see the lever. The lesson I learned from this event is to wait for the CAS message to appear after the captain says ON for the parking brake and to make sure nobody tries to undo the parking brake at the end of the flight without us going outside and verifying chocks. I did go and hover my hand towards the emergency brake but that was unnecessary since the airplane had already came to a stop so I did not pull it. Chief Pilot was notified of the event.