VFR JET RANGER IN IMC MANEUVERS ON TO ILS AT 1000 FT AGL CAUSING NMAC WITH RPTR'S MD-80.

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WHILE TRACKING THE ILS TO LGA'S RWY 13; WE RECEIVED A TCASII 'TFC' WARNING AT APPROX 1300 FT AGL; OUR TCASII SCREEN INDICATED TFC LESS THAN 2 MI AHEAD; 500 FT BELOW US. WITHIN ABOUT 20 SECONDS; TCASII BEGAN ISSUING AN 'RA' ON SAME TFC; COMMANDING US TO 'MONITOR VERT SPD.' (TCASII WAS CALLING FOR US TO LEVEL OFF). AT THIS POINT; TCASII SHOWED TFC TO BE AT OUR 12:30 POS AND 300 FT BELOW US; LESS THAN 1 MI AHEAD. WE WERE ABOUT 1100 FT AGL. ALMOST IMMEDIATELY AFTER ABOVE 'RA' A SECOND 'RA' WAS RECEIVED COMMANDING 'CLB; CLB.' AS I WAS PWRING UP THE ENGS AND PULLING UP; FO SAW A BELL JET RANGER DIVING AWAY FROM US. (WE WERE CLOSE ENOUGH TO GET A COMPLETE DESCRIPTION OF ACFT DESPITE 1 3/4 MI VISIBILITY). TCASII INDICATED THAT WE PASSED 200 FT DIRECTLY OVERTOP OF BELL HELI MEANING HAD WE NOT HAVE HAD TCASII; OUR MD-80 WOULD HAVE COLLIDED WITH A HELI THAT WAS OPERATING VFR; EXACTLY IN THE CTR OF AN OPERATIONAL ILS APCH. TWR SUPVR SAID THAT ROTORCRAFT WILL OPERATE VFR ON PROCS THAT UNDERLAY THIS APCH. THIS PARTICULAR HELI CLBED UP INTO ILS CORRIDOR; UNAUTH. TWR SHOULD HAVE ADVISED US TO EXPECT TCASII TFC PASSING BELOW US; WHILE ON ILS. EVEN THOUGH WE STILL WOULD HAVE HAD TO PULL UP; WE WOULD HAVE BEEN MORE PREPARED; AS NO ONE EXPECTED TO HAVE TFC BELOW YOU WHILE DOING AN ILS.