CAPT OF A CPR TWIN TURBINE HELI WAS INFORMED BY THE JFK TWR THAT HE HAD NOT FLOWN DURING APCH TO LAND THE RTE INTENDED OVER ACTIVE RWY 31L.

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OUR FLT WAS FROM OUR CPR HELIPAD TO JFK. APPROX 19 MI FROM JFK; THE FO (PNF) CONTACTED JFK TWR ON 119.10. WE WERE CLRED TO ENTER JFK CLASS B AIRSPACE AT OR BELOW 500 FT MSL VIA THE CONEY RTE TO AND REMAIN S OF RWY 31L AT THE APCH END OF RWY 4L. APPROX 1 MI SW OF THE APCH END OF RWY 4L; JFK TWR CLRED US OVER THE APCH END OF RWY 31L TO THE GA TERMINAL HELIPAD. I FLEW OVER THE APCH END OF RWY 31L BTWN THE LNDG THRESHOLD AND WHERE DEPARTING ACFT WERE LINING UP FOR DEP. I DID NOT OVERFLY ACFT ON THE GND. I THEN TURNED NW TO PARALLEL RWY 31L BTWN RWY 31L AND THE ATC TWR. ABEAM THE TWR; THE CTLR QUERIED ME AS TO WHERE I WAS AND WHERE I WAS GOING. I STATED THAT I HAD BEEN CLRED ACROSS THE APCH END OF RWY 31L TO LAND AT GA TERMINAL AND THAT WAS WHAT I WAS DOING. THE CTLR INFERRED BY THE TONE OF HIS VOICE THAT I HAD NOT BEEN CLRED TO CROSS RWY 31L; BUT CLRED AROUND THE END OF RWY 31L. HE ASKED WHERE I WAS; AND I REPLIED I WAS BTWN THE TWR AND RWY 31L. AT THAT POINT; HE CLRED ME 'TO LAND PLT'S DISCRETION AT GA TERMINAL; AREA NOT VISIBLE FROM THE TWR.' I FEEL I COMPLIED WITH TWR'S INSTRUCTIONS BY MY FLT PATH; HOWEVER; FROM HIS REACTION IT IS MY JUDGEMENT NOW THAT HE WANTED ME TO FLY AROUND THE END OF RWY 31L AND NOT OVER THE DISPLACED THRESHOLD PORTION FO RWY 31L. AT NO TIME PRIOR TO MY XING RWY 31L DID THE CTLR TELL ME TO FLY AROUND THE END OF RWY 31L. HIS WORDS WERE 'OVER THE APCH END OF RWY 31L.' LCL CTL WAS EXTREMELY BUSY AT THE TIME OF THIS INCIDENT WITH NUMEROUS ARRS AND DEPS. THE ROUTING HE GAVE US IS A STANDARD ROUTING TO GA TERMINAL WHEN RWY 31 IS IN USE. IN THE FUTURE; I WILL ENSURE THAT THE CLRNC IS READ BACK AND NOT JUST ROGER AN APCH AND LNDG CLRNC WHEN XING THE APCH END OF AN ACTIVE RWY. LIKEWISE; ATC MUST BE CLR BOUT WHEN TO FLY AROUND OR OVER A RWY.