FLC OF CPR CL601-3A-ER HAS TCASII TA THEN RA TO DSND AND RESPONDS. IN LATER COM WITH ATC IT IS INDICATED THERE WAS NO KNOWN TFC IN THE AREA.

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WHILE STRAIGHT AND LEVEL AT 13000 FT ON THE ARR ROUTING FOR HPN; A TCASII AURAL TA WAS RECEIVED. UPON CONSULTING THE TCASII INDICATOR A RED INTRUDING TARGET WAS OBSERVED AT OUR 12 O'CLOCK POS; LESS THAN 2 MI IN RANGE; WITH IDENTICAL ALT AND NO VERT TREND. IN VIEW OF THE EXTREME PROX OF THE TARGET AND AT MY URGING; THE FO (PF) DISCONNECTED THE AUTOPLT IN PREPARATION FOR EVASIVE ACTION. ALMOST IMMEDIATELY; BOTH AURAL AND VISUAL TCASII RA INFO WAS RECEIVED. THIS INFO INDICATED A REQUIRED DSCNT RATE OF 2500 FPM OR GREATER TO ESCAPE THE INTRUDING TARGET. DURING THE COURSE OF OUR COMPLIANCE WITH THE TCASII RA; THE INTRUDING TARGET BEGAN TO DISPLAY A DSNDING TREND ARROW; RETAINED ITS RELATIVE BEARING AND DISTANCE; AND CONTINUED TO SHOW VERT SEPARATION OF ZERO. IN RESPONSE; THE TCASII ISSUED AN INCREASED DSCNT RATE COMMAND OF 3500 FPM OR GREATER. UPON ACHIEVING THE REQUIRED RATE OF DSCNT THE INTRUDING TARGET DISAPPEARED FROM THE DISPLAY AND THE TCASII AURAL ADVISORY; 'CLR OF CONFLICT' WAS RECEIVED. AT THE CONCLUSION OF OUR EVASIVE ACTION WE WERE AT AN ALT OF 10400 FT. DURING THE DSCNT FROM OUR ASSIGNED ALT OF 13000 FT I MADE 2 ATTEMPTS TO CONTACT ZBW TO ADVISE THEM OF OUR ACTIONS; BOTH WITHOUT RESPONSE. AFTER OUR EVASIVE ACTION I AGAIN CALLED ZBW. IMMEDIATELY FOLLOWING THIS XMISSION (MY THIRD) WE WERE ISSUED INSTRUCTIONS TO FLY A HEADING REPRESENTING A 90 DEG TURN TO OUR R AND A DSCNT TO 9000 FT BUT RECEIVED NO ACKNOWLEDGMENT OF THE CALL JUST MADE. WHEN READING BACK THE NEWLY ASSIGNED HEADING AND ALT I ASKED THE CTLR IF WE COULD PASS ALONG A MESSAGE RELATIVE TO OUR ACTIONS. HE RESPONDED THAT HIS WORKLOAD WAS TOO GREAT TO TAKE ANY MESSAGES AT THAT TIME. WE CONTINUED ON THE ASSIGNED HEADING AT THE ASSIGNED ALT FOR ABOUT A MIN AT WHICH TIME THE CTLR ASKED US TO PROCEED WITH OUR MESSAGE. AFTER INDICATING WE HAD DEPARTED OUR ORIGINALLY ASSIGNED ALT OF 13000 FT TO COMPLY WITH A TCASII RA THE CTLR INDICATED THAT NO PROBS HAD BEEN CAUSED BY OUR ACTIONS BUT THAT HE HAD NOT OBSERVED ANY TFC IN OUR IMMEDIATE VICINITY. SIMILARLY; NEITHER THE FO NOR I WERE ABLE TO ACQUIRE THE INTRUDING TARGET VISUALLY DURING THE EVENT ALTHOUGH OUR ABILITY TO DO SO MAY HAVE BEEN COMPROMISED BY THE FACT IT WAS DUSK AND BY OUR NEED TO MONITOR THE TARGET ON THE TCASII SYS.