DURING PUSHBACK AND ENG START PROCS; A CL65 MOVES FORWARD AND CONTACTS THE TUG; DAMAGING THE ACFT AT CRP; TX.

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DURING PUSHBACK ON RAMP IN CRP; THE TUG OPERATOR PUSHED THE ACFT TO AN UNUSUAL FINISHING POINT. THE CAPT QUERIED THE RAMP PERSONNEL AS TO OUR ABILITY TO TAXI OUT SAFELY AND WERE ASSURED WE WERE LINED UP CORRECTLY. DURING ENG START; WHICH IS MY RESPONSIBILITY; THE CAPT ATTEMPTED TO CONTACT RAMP PERSONNEL TO SEE IF WE WERE STILL CONNECTED TO THE TUG. I RESPONDED THAT THE RAMPER HAD ALREADY REMOVED HIS HEADSETS. THERE WAS NO CONFIRMATION FROM RAMP THAT WE WERE OR ALREADY WERE DISCONNECTED. AS I FINISHED THE ENG START; WE BEGAN TO ROLL FORWARD. I IMMEDIATELY YELLED 'BRAKES' AND APPLIED BRAKES. HOWEVER; WE HAD ROLLED FORWARD AND IMPACTED THE TUG. RAMP ACKNOWLEDGED THAT SHE NEVER INSTRUCTED US TO SET OUR PARKING BRAKE AND THAT PUSH WAS COMPLETE. SUPPLEMENTAL INFO FROM ACN 613459: DURING PUSHBACK PROC; WHILE ACFT WAS AT REST; I INQUIRED WHETHER THE NOSEWHEEL WAS STRAIGHT. TUG DRIVER RESPONDED THAT THE ACFT WOULD BE ABLE TO MANEUVER OUT ON ITS OWN. AT NO TIME DID THE TUG DRIVER STATE THAT THE PUSHBACK WAS COMPLETE AND TO SET BRAKES. TOWBAR WAS DISCONNECTED BEFORE BRAKE WAS SET. THE ACFT ROLLED FORWARD AND CONTACTED TUG. I IMMEDIATELY SET BRAKE. I SHUT DOWN THE ENGS AND EXITED THE ACFT TO INSPECT THE SCENE. THERE APPEARED TO BE DAMAGE TO THE FUSELAGE IN THE NOSE AREA -- APPROX A 2 FT LONG CREASE. I DID NOT NOTICE ANY DAMAGE TO THE TUG. THERE WERE NO RPTS OF ANY INJURIES.