FALCON DA50 HAS A TCAS RA DURING VISUAL APCH TO HVN.

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I WAS THE PIC OF A FALCON 50FX ON AN IFR FLT PLAN FROM SDL TO HVN. THIS WAS THE FIRST LEG OF A 2-LEG TRIP AND BOTH PLTS HAD AN ADEQUATE REST PERIOD PRIOR TO THE FLT. CURRENT WX AT NEW HAVEN WAS WINDS 210 DEGS AT 6 KTS; CLR SKIES AND A RPTED VISIBILITY OF 6 NM IN HAZE. UPON CHKING IN WITH NEW YORK APCH; WE WERE TOLD TO EXPECT A VISUAL APCH TO RWY 20. NEARING THE NEW HAVEN AREA WE WERE AT 3000 FT AND ON A HDG OF 150 DEGS ASSIGNED AND TOLD TO RPT THE ARPT IN SIGHT. THE CTLR STATED THAT THIS HDG WOULD GIVE US A 2-3 MI FINAL. APPROX 3 MI FROM THE ARPT; WE TOLD NEW YORK THAT WE HAD THE ARPT IN SIGHT. NEW YORK APCH ACKNOWLEDGED CLRED US FOR THE VISUAL APCH AND INSTRUCTED US TO SWITCH FREQS TO NEW HAVEN TWR. AFTER TRYING TO CHK IN WITH TWR ON THE NEW YORK APCH FREQ (CREW FAILED TO CHANGE TO TWR FREQ). WE THEN CHKED IN WITH NEW HAVEN TWR. WE WERE NOW APPROX 2 NM NW OF THE ARPT ON A SLIGHT R DOGLEG TO FINAL. THE TWR OPERATOR INITIALLY ASKED US FOR OUR POS AND THEN SAID THAT HE HAD US IN SIGHT. AT THE SAME TIME AS OUR ARR; 2 LIGHT SINGLE ENG ACFT WERE IN A L-HAND PATTERN MAKING TOUCH-AND-GO APCHS TO RWY 20. ONE AIRPLANE; A WARRIOR (I BELIEVE) WAS TURNING L BASE TO FINAL AS WE APCHED THE ARPT. THE TWR CTLR TOLD THE WARRIOR TO MAKER A L 360 DEG TURN FOR TFC. UPON SIGHTING THE POTENTIAL CONFLICT; WE LEVELED OFF OUR DSCNT AT 1000 FT MSL AWAITING LNDG CLRNC. ONCE THE WARRIOR BEGAN HIS L 360 DEG TURN; WE RECEIVED AN RA 'MONITOR VERT SPD.' WE CONTINUED TO FLY TOWARDS THE RWY AT 1000 FT MSL; WITHIN THE GREEN ARC CALLED FOR BY THE RA. WHEN WE RECEIVED OUR CLRNC TO LAND; WE WERE NOT IN A POS TO MAKE A SAFE LNDG SO WE REQUESTED A GAR. THE TWR CLRED US FOR A R TFC PATTERN AND WE CAME AROUND AND LANDED WITHOUT INCIDENT. FROM THE COCKPIT; THE KEY CONTRIBUTORS TO THIS CONFLICT APPEAR TO BE: 1) WX. THE HAZE PREVENTED US FROM PICKING UP THE ARPT UNTIL LATER THAN NORMAL; LEADING TO A LATE HDOF FROM NEW YORK APCH TO NEW HAVEN TWR. 2) INITIAL CONFUSION FROM NEW HAVEN TWR REGARDING OUR LOCATION. WHEN CHKING IN; WE ONLY PROVIDED OUR CALL SIGN WITH NO LOCATION GIVEN; ASSUMING THAT NEW YORK APCH HAD COORD THE IFR HDOF. THIS ADDED TO THE CONFUSION OF INTEGRATING OUR IFR ARR WITH THE VFR TFC IN THE PATTERN. OUR 'LATE ARR' INTO THE TFC PATTERN MADE IT EXTREMELY DIFFICULT ON THE CTLR TO SEQUENCE 2 ACFT ON SHORT APCH TO THE SAME RWY. THE RA 'MONITOR VERT SPD' ONCE AGAIN PROVES THE INCREDIBLE VALUE OF TCAS. ALTHOUGH I BELIEVE THAT A SIMILAR OUTCOME WOULD HAVE RESULTED THROUGH SEE AND AVOID; THE RA MADE THE RESOLUTION MUCH LESS STRESSFUL AND SAFER.