AIR CARRIER CREW CROSSED HPN RUNWAY 16-34 AFTER ALLEGED RECEIVING CLEARANCE FROM GROUND CONTROL; CONFUSION WHETHER THEY WERE CLEARED TO CROSS OR NOT WAS THE RESULT.

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WE WERE ISSUED A TAXI CLRNC BY HPN GND TO TURN R ON TXWY A AND L ON TXWY D TO HOLD SHORT OF RWY 16/34. AT TXWY D; WE STOPPED AND AWAITED FURTHER INSTRUCTIONS AND WHEN GND TOLD US TO PROCEED; I TAXIED ACROSS RWY 16/34 AND MADE A L ON TXWY L AS INSTRUCTED. WHILE WAITING ON TXWY D; WE WERE FACING NW AND I COULD NOT SEE THE STARTING POINT OF RWY 34 TILL WE WERE MAKING THE L TURN. AT THAT TIME; I NOTICED AN ACFT IN POSITION ON RWY 34 THAT SEEMED TO BE READY FOR TKOF. AFTER WE HAD CROSSED RWY 16/34 AND WERE TAXIING S ON TXWY L; WE NOTICED THE ACFT IN POSITION ON RWY 34 WAS COMING DOWN THE RWY AND SEEMED TO BE ABORTING A TKOF. MY FO AND I QUESTIONED WHAT HAD HAPPENED AND WE CONCURRED WE HAD OUR CLRNC TO CROSS AND WE WERE NOT ISSUED ANY WARNINGS BY THE GND CTLR OF ANY INCURSION WE MIGHT HAVE CAUSED. WE THEN CONTACTED TWR FREQ AND RECEIVED CLRNC TO CROSS RWY 11/29 AND TAXI INTO THE RWY 34 PAD AND WAIT TKOF CLRNC DUE TO WX DELAYS. NO MENTION WAS DONE FROM ATC DURING THE NEXT 20 MINS OF GND DELAY AND THEN WE RECEIVED OUR TKOF CLRNC. I BELIEVE THE INCURSION HAPPENED DUE TO A CLRNC MISINTERP BTWN ME AND THE GND CTLR OF WHERE TO HOLD SHORT AND WHEN TO PROCEED. I BELIEVE IT NEEDS TO BE HIGHLIGHTED THAT EVERY CLRNC TO CROSS AN ACTIVE RWY MUST ONLY BE MADE BY THE TWR CTLR. I BELIEVE IT IS IMPERATIVE IT WILL BECOME COMMON PRACTICE AT ALL ARPTS TODAY THAT ONLY THE TWR CTLRS CAN GIVE RWY XING CLRNCS AND NOT THE GND CTLR. THAT IS THE PRACTICE AT MAJOR ARPTS WE FLY INTO AND IT SHOULD BECOME COMMON STANDARDS AT ALL ARPTS.