AN ACR FLC RECEIVED A TCASII RA WHILE OPERATING NEAR THE FLOOR OF CLASS B AIRSPACE IN IMC.

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ON BASE LEG TO ILS RWY 4R BOSTON. HDG 310 DEGS AT 3000 FT TOLD TO INTERCEPT LOC. TFC CALLED AT 2700 FT 10 O'CLOCK IDENTED TFC ON TCASII. TCASII ALERTED 'TFC; TFC;' THEN ANNOUNCED; 'DSND XING DSND.' CAPT FLYING FOLLOWED VSI COMMAND TO APPROX 1200 FPM DOWN. FO (ME) CALLED ATC AND INFORMED WE FOLLOWED TCASII AND LEVELED AT 2500 FT AFTER TCASII ANNOUNCED; 'CLR OF CONFLICT;' CLOSEST DISTANCE FROM TARGET WAS APPROX 1 1/2 - 2 MI. CALLED ATC AND SAID WE WERE GOING BACK TO 3000 FT. HE THEN SAID TO MAINTAIN 2500 FT AND CLRED FOR THE APCH. (HE SEEMED IRRITATED A LITTLE BUT MADE NO FURTHER COMMENT). WE NEVER ACQUIRED TFC VISUALLY. CONTINUED APCH AND LNDG WITHOUT INCIDENT. ON GND; GND CTLR REQUESTED US TO CALL TRACON. CTLR WAS CURIOUS WHY WE HAD DSNDED AND NOT CLBED. CAPT; SAID WE WERE FOLLOWING OUR RA AS PER OUR COMPANY POLICY. THE ACFT APPARENTLY WAS DEPARTING NORWOOD ARPT AND WAS ONLY 300 FT BELOW FLOOR OF CLASS B ON APCH CORRIDOR FOR RWY 4R. UNDER IMC DEPS FROM NORWOOD SHOULD BE RESTR TO LOWER ALTS. POSSIBLY OTHER ACFT WAS CLBING INTO OUR ALT PRECIPITATING THE RA. OVERALL; GOOD JOB BY FLC AND COCKPIT RESOURCE MGMNT WAS EXCELLENT.