AN MD88 TCASII ALERTS THE CREW OF A POTENTIAL CONFLICT WHEN AN OPPOSITE DIRECTION GA ACFT CLBS THROUGH THEIR ALT 8 NM NE OF BDL; CT.

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WE WERE ON RADAR DOWNWIND TO BDL AT 5000 FT MSL ON A 110 DEG HDG. WE NOTICED POP-UP TFC ON TCASII AT 12 O'CLOCK; APPROX 7 NM AND 500 FT BELOW OUR ALT. THE PNF (CAPT) CALLED APCH TO CONFIRM THE VFR ACFT. BEFORE TRACON COULD REPLY; THE PROB ACFT BEGAN TO CLB; INITIATING A TCASII TA FOLLOWED IMMEDIATELY BY AN RA. WE INITIATED A LEVEL L-HAND TURN; FOLLOWED BY A TCASII COMMAND TO DSND. ANOTHER CALL WAS MADE TO TRACON WITH NO RESPONSE. WE DSNDED TO ABOUT 4500 FT MSL UNTIL THE TCASII WARNING CLRED. ON OUR THIRD CALL TO ADVISE TRACON OF OUR EVASIVE MANEUVER; THEY RESPONDED WITH A VECTOR TOWARDS THE FIELD. A SCATTERED CLOUD LAYER AT 5000 FT MSL MADE VISUAL IDENT OF PROB ACFT VERY DIFFICULT. WE PROCEEDED TO ARPT FOR A VISUAL APCH AND LNDG ON RWY 24 AT BDL. A POSTFLT PHONE CALL TO THE TRACON REVEALED THE ACFT WAS OUTSIDE OF CLASS C AND NOT PARTICIPATING IN ANY SVC. TRACON RPTED THEY ATTEMPTED TO RPT ACFT AND CALLS WENT UNANSWERED. WE MAY HAVE BLOCKED EACH OTHER. SUPPLEMENTAL INFO FROM ACN 544405: DSNDED TO APPROX 4500 FT. I MADE ANOTHER RADIO CALL TO ADVISE OF OUR COMPLYING WITH RA. APCH SAID OK AND SOMETHING ABOUT TFC AT 4000 FT.