FLC TAKES EVASIVE ACTION AS TCASII ISSUES CLB.

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WE HAD BEEN CLRED DIRECT LGA EARLIER AT 7000 FT. APCH CTL SAID TO DSND TO 6000 FT AND COME L TO A HDG. THE TURN WAS APPROX 40 DEGS L. WE ROGERED. A FEW MOMENTS LATER HE GAVE US TFC; AT 12:30; CLBING VFR TO 6500 FT. IT WAS A EMB120 ACFT. I DID NOT SEE HIM SO I LOOKED AT MY TCASII. THERE WAS A TARGET; 1300 FT AT 12:30. IMMEDIATELY IT BECAME TCASII 'TFC; TFC.' WE WERE IN THE TURN AND DSNDING THROUGH ABOUT 6800 FT MSL. I LOOKED OUTSIDE AND SAW THE ACFT ON THE NOSE AND CLOSING RAPIDLY. THE TCASII NOW SAID; 'CLB; CLB' AND I DISCONNECTED THE AUTOPLT TO INCREASE THE BANK ANGLE AND CLB. I VISUALLY AVOIDED THE ACFT PASSING 500 FT N OF HIM AND ZERO ALT DIFFERENCE.HAD WE BEEN IMC; WE WOULD HAVE PASSED EXTREMELY CLOSE IF NOT IMPACTED EACH OTHER. THE EMB DID NOT APPEAR TO MANEUVER TO AVOID US AT ALL. AFTER ARR AT LGA; I CALLED APCH ON THE LANDLINE TO GET MORE INFO AND EXPRESS MY CONCERN WITH OUR CTL AT THAT POINT. WE DID NOT HESITATE TO TURN OR DSND WHEN CLRED AND YET WE VERY NEARLY HIT THE VFR CLBING ACFT. THERE WAS A STRONG TAILWIND FOR US WHICH COULD HAVE AGGRAVATED THE CTLR'S PLAN FOR US TO HAVE BETTER SEPARATION. A TURN CALL 10 MI EARLIER WOULD HAVE BEEN THE BEST CALL.