WHILE COMPLETING THE PREDEP COCKPIT DUTIES; THE FO AND THE RPTR NOTICED THE ACFT MOVE. THE CAPT QUICKLY SET THE PARKING BRAKE; BUT NOT BEFORE THE ACFT HAD MOVED ABOUT 4 FT AND DAMAGED THE FORWARD ENTRY DOOR ON THE JETWAY. JFK IS THE ONLY PLACE IN THE COMPANY SYS WHERE THE BRAKES ARE TO BE LEFT SET AT ALL TIMES AT THE GATE. THE CHOCKS WERE REMOVED WITHOUT COM WITH THE COCKPIT. THE TUG WAS CONNECTED; BUT THE BRAKES WERE NOT SET. ONE OF THE 3 CHOCKS WAS A SMALL CHOCK.

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FO X AND I ARRIVED AT THE GATE AT JFK FOR AN MD88 FLT. THE FO WENT OUT TO DO THE WALKAROUND WHILE I BRIEFED THE FLT ATTENDANTS AND CHATTED A BIT. I ENTERED THE COCKPIT AND STARTED THE OVERHEAD FLOW PATTERN. THE FO RETURNED; ANNOUNCED CHK COMPLETE; TUG HOOKED UP; AND CHOCKS INSTALLED. WE COMPLETED THE COCKPIT CHKS AND LOADED THE FMS. BOARDING WAS COMPLETED 10 MINS BEFORE PUSHBACK. THE FLT ATTENDANT ENTERED WITH A SMALL CATERING PROB. WE DISCUSSED IT AND THEN WERE DIRECTED TO CONTACT CLRNC FOR A FULL RTE RERTE. AFTER WE BOTH COPIED THE CLRNC I STARTED ENTERING THE POINTS AS THE FO READ THEM OFF. THE FO HEARD A CRUNCHING NOISE AND LOOKED UP TO SEE THE JETWAY SEEMING TO HAVE MOVED AWAY. HE YELLED; HEY.... I GLANCED UP AND HIT THE BRAKES AND I SET THE PARKING BRAKE HANDLE. I DO NOT KNOW IF THE PARKING BRAKE WAS SET OR NOT; I DO NOT REMEMBER KNOCKING IT OFF OR EVEN LOOKING AT IT. OUR GREEN PAGES DIRECT US TO SET THE BRAKES AND I BELIEVE THEY WERE! THE DRIVER WAS SITTING ON THE TUG WAVING WHEN I LOOKED OUT; WE HAD SLIPPED BACK 4 FT WITH THE DOOR (FORWARD ENTRY) ENCOUNTERING THE SIDE OF THE JETWAY. WE HAD NOT SENSED ANY MOVEMENT NOR ANY IMPACT; BUT HAD HEARD THE PLASTIC LINER ON THE DOOR CRUMP. I WENT DOWN THE BACK STAIRS (STILL DOWN); SAW A LARGE CHOCK UNDER THE L MAIN AND NOSEWHEEL AND A SMALL CHOCK UNDER THE OUTBOARD R MAIN. ALSO THE TUG WAS STILL HOOKED UP. I HONESTLY DON'T KNOW HOW WE SLID BACKWARD. 1 GND CREWMAN SAID THEY HAD PULLED THE MAIN CHOCKS BUT PUT IT BACK WHEN MOTION WAS DETECTED. NO ONE WAS ON THE JETWAY OR STANDING NEAR THE DOOR AT THE TIME OF THE INCIDENT; ALL PAX WERE SEATED AND UNAWARE OF THE DAMAGE TO THE DOOR UNTIL I MADE A PA. JFK IS THE ONLY CITY WE HAVE TO SET THE PARKING BRAKES. A SIGN SHOULD BE PAINTED OUTSIDE AS A REMINDER. CHOCKS SHOULD NOT BE REMOVED UNTIL COMS ARE ESTABLISHED WITH THE COCKPIT CREW. FULL SIZE CHOCKS SHOULD BE USED ON ALL WHEELS. THE TUG'S BRAKES SHOULD BE SET AT ALL TIMES. I AM NOT SURE IF ANY OF THIS WAS NOT DONE.