CAPT OF A320 PREMATURELY RELEASES PARKING BRAKES BASED ON HAND SIGNALS FROM RAMP PERSON.

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I STARTED DAY IN FLL WITH AN EARLY EAST COAST GET UP. THE CREW DESK REASSIGNED ME AN ADD-ON LEG. I HAD TO RUSH FROM THE GATE TO THIS FLT WITH A 54 MIN SCHEDULED CONNECTION AND ALSO HAD TO GO TO OPS TO PICK UP DEADHEAD TICKETS FOR LEG HOME. I GOT TO GATE X ABOUT 45 MINS BEFORE DEP. I MET THE FO. ALL SEEMED NORMAL. NO ONE FROM THE PUSHBACK CREW ADVISED ME OR THE FO THAT THEIR HEADSET COM WAS INOP. A DENVER RAMP PERSON GAVE ME THE HAND SIGNAL TO RELEASE THE BRAKES. I ACKNOWLEDGED AND RELEASED THE BRAKES. I ASSUMED IT WAS CHOCKED OR SECURED TO THE TUG. THE ACFT STARTED TO ROLL BACKWARDS; THEREFORE I PUT THE BRAKES BACK ON AND SIGNALED WITH HAND SIGNALS AND ALSO ON THE INTERPHONE TO STOP. WE HAD NOT CALLED DENVER RAMP CTL FOR A CLRNC TO PUSH. I BELIEVE THE PUSH BACK CREW MUST (FOR SAFETY REASONS) COMMUNICATE WITH THE COCKPIT IN PERSON IF THEIR HEADSET IS INOP PRIOR TO COMMENCING PUSHBACK. THE COCKPIT CREW HAS LEARNED THAT THE RELEASE BRAKES HAND SIGNAL NORMALLY MEANS THE ACFT IS CHOCKED. NO DAMAGE WAS DONE OR ANYONE HURT; BUT THE MISCOM WAS VERY SCARY. IN THE FUTURE THE PUSHBACK CREW SHOULD VISIT THE FLT DECK IN ADVANCE IF ANYTHING UNUSUAL IS PLANNED FOR THE PUSHBACK. THE PLT'S FOM AND PUSHBACK CREW'S MANUAL MUST BE REWRITTEN TO CLARIFY THIS STEP. ALSO ALL PARTICIPANTS MUST BE TAUGHT THE IMPORTANCE OF PRE-PUSHBACK VERBAL OR FACE TO FACE DISCUSSION IF ANYTHING UNUSUAL IS PLANNED. ADDITIONALLY; WHY ARE WE PUSHING BACK AT A MAJOR ARPT WITH AN INOP HEADSET? IS THE TIME SAVINGS WORTH THE SAFETY RISK?