SF340B FLC INITIATE TCASII EVASIVE MANEUVER DUE TO CONFLICTING SINGLE ENG CESSNA ON AN INTERCEPTING TFC PATTERN TO ANOTHER RWY.

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APPROX 6 MI SW OF SGF ARPT AT 3000 FT MSL; WE CALLED ARPT IN SIGHT. THE APCH CTLR CLRED US FOR THE VISUAL APCH TO RWY 20 AND HANDED US OFF TO SGF TWR. UPON CHKING IN WITH SGF TWR; WE WERE CLRED TO LAND ON RWY 20. AT THE SAME TIME; THE CTLR TOLD A CESSNA TO MAKE 'L CLOSE TFC.' ON R DOWNWIND FOR RWY 20; TWR INFORMED THE CESSNA OF SAAB 340 (US) TFC. THE CESSNA RPTED TFC IN SIGHT AND WAS TOLD BY SGF TWR TO MAINTAIN VISUAL SEPARATION WITH TFC. THE CESSNA SAID THEY WOULD MAINTAIN VISUAL WITH US. SGF TWR CALLED OUT THE TFC FOR US. WE DID NOT HAVE THE TFC IN SIGHT BUT 'ROGERED' THE CALL. AS WE SLOWED; IN LNDG CONFIGN; TURNED R BASE AND DSNDED FOR RWY 20; A TA APPEARED ON OUR TCASII -- AT CO-ALT OF 2300 FT MSL AT LESS THAN 2 MI. THIS TA IMMEDIATELY TURNED INTO A 'CLB' RA OF 2000 FPM. WE COMPLIED WITH THE RA; INFORMED TWR OF THE RA; AND FINALLY SPOTTED TFC OFF OUR R; APPROX 1/4 MI AWAY. WE CONTINUED AND LANDED UNEVENTFULLY ON RWY 20. THE CAPT SPOKE WITH TWR SUPVR UPON LNDG. THE TWR WAS RUNNING A L-HAND PATTERN FOR RWY 14 AND A R-HAND PATTERN FOR RWY 20. THE ACFT ON RWY 14 DOWNWIND BLENDED IN WITH CITY LIGHTS E OF THE ARPT. I BELIEVE THE PATTERNS SHOULD BE BOTH R- OR L-HAND TFC WHEN UTILIZING CROSS RWYS. SUPPLEMENTAL INFO FROM ACN 464562: I SPOKE WITH TWR AND WE DISCUSSED WAYS TO AVOID THIS IN THE FUTURE. I THINK TWR SHOULD USE A L-HAND PATTERN FOR RWY 14 WHEN ACFT ARE LNDG AND DOING A R-HAND PATTERN FOR RWY 20; REDUCING THE POSSIBILITY OF THIS RECURRING AGAIN. DESPITE GOOD VISIBILITY; THIS ACFT BLENDED IN WITH GND CLUTTER LIGHTS; MAKING DETECTION VISUALLY DIFFICULT.