CE-680A First Officer reported the aircraft rolled free of the improperly placed chocks and made contact with another parked aircraft.

Narrative

The ramp was very busy. The line person had us pull the plane nose-in to the FBO. He threw some chocks under our nose wheel and we disembarked our passengers. We proceeded to begin completing all of the activities associated with securing the aircraft. We also asked the same line person who chocked our aircraft for fuel and a lavatory service. He left to go finish servicing another aircraft and then returned with the lavatory cart to service our lavatory. We had the aircraft completely shut down with all of the plugs and covers installed; hydraulic accumulator bled off; and torque link disconnected. The Captain and I were inside and all that was remaining to secure the aircraft before we closed; sealed; and locked the door was to release the brakes and then disconnect the batteries. I was proceeding down the stairs when the Captain released the brakes and the aircraft rolled backwards. We did not notice that the chocks were loosely installed and only behind the right tire of the nose wheel assembly. When the aircraft rolled backwards; the right nose wheel tire hit the chocks; the nose wheel assembly turned and the aircraft rolled out of the chocks. The aircraft continued rolling backwards while the Captain was attempting to start the APU so that he could engage the brakes. I jumped off of the stairs and attempted to slow the aircraft from rolling by pushing forward on the aft portion of the stairs. The plane kept rolling and the right wingtip scratched the side of another aircraft. The wingtip of our aircraft was damaged but it appears the other aircraft was only scratched.Before releasing the brakes from now on; I will ensure we are properly chocked. In addition some additional training needs to occur for the line persons on how to properly chock an aircraft.