LGT IN IMC HAS TCASII RA WHEN CLRED FOR AND STARTING DSCNT. RESPONDS WITH CLB.

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CLRED TO DSND FROM 13000-11000 FT. STARTED DSCNT TO ABOUT 12400 WHEN TCASII CALLED 'TFC.' SHORTLY THEREAFTER (5 SECONDS) TCASII ISSUED RA TO CLB. CLB WAS INITIATED AS TFC WAS SHOWING -- 400 FT ON TCASII. BY THE TIME A POS RATE WAS INDICATED; THE TFC WAS MINUS 200 FT. CAPT LOOKED OUT AND SAW WHAT APPEARED TO BE SMALL BUSINESS JET WITHIN 3-4 MI AND CLOSING RAPIDLY DIRECTLY IN OUR FLT PATH. AS IT PASSED BENEATH US; IT WAS 400-500 FT.BELOW. HE MADE NO EVASIVE MANEUVER AND APPEARED NOT TO SEE US. I INFORMED CTLR WE WERE CLBING AS DIRECTED BY TCASII; HE SAID HE HAD NO TFC IN OUR AREA. LATER HE CALLED BACK AND SAID HE HAD NOT SEEN THE TFC WHICH CAUSED THE CONFLICT. WE CLBED TO 13400 BEFORE AGAIN COMMENCING DSCNT. CONTINUED ON TO LGA AND LANDED WITHOUT INCIDENT. THERE IS LITTLE DOUBT WE MAY HAVE HAD A MID-AIR IF IT HAD NOT BEEN FOR TCASII. SUPPLEMENTAL INFO FORM ACN 271057: ATC STATED THEY WERE UNAWARE OF HIS PRESENCE ALTHOUGH OUR TCASII PICKED UP HIS MODE C XPONDER. HAD WE DSNDED AS INSTRUCTED TO 11000; WE MAY HAVE CROSSED HIS FLT PATH AND HAD A POSSIBLE NEAR MISS/INCIDENT/ACCIDENT. THANKS TO TCASII WE CAN TELL THIS STORY!