NMAC DURING A MULTIPLE RWY OP PARALLEL RWYS. POSSIBLE CLRNC INTERP PROB. OP ERROR INVOLVED.

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GRR APCH CTL CLRED FLT DOWN TO 2500 FT MSL. WE WERE PREVIOUSLY CLRED RNAV DIRECT TO THE ARPT. APPROX 8 MI SW OF THE ARPT; APCH CTL ASKED IF WE HAD THE ARPT IN SIGHT. WE ACKNOWLEDGED THAT WE DID. APCH THEN CLRED OUR FLT FOR THE VISUAL APCH TO RWY 8R KGRR AND ADVISED US THERE WAS A SINGLE ENG CESSNA ON THE VISUAL TO RWY 8L. WE ACKNOWLEDGED AND INTERCEPTED THE LOC APPROX 4 MI SW OF THE ARPT. WE CONTINUED INBOUND VISUALLY WITH THE ILS FOR GUIDANCE. NOTE: AT NO TIME DID OUR ACFT DRIFT N OF THE RWY 8R EXTENDED CTRLINE. IT APPEARED TO MYSELF AND THE FO THAT THE SINGLE ENG CESSNA OVERSHOT FINAL APCH FOR RWY 8L AND WAS ENCROACHING UPON OUR AIRSPACE. THE FO QUESTIONED APCH CTL AGAIN AND WAS ADVISED THAT THE OTHER ACFT WAS PROCEEDING TO RWY 8L. SHE THEN HANDED US OFF TO THE LCL CTLR. WE MOMENTARILY LOST VISUAL CONTACT WITH THE INTRUDING ACFT AND ALMOST IMMEDIATELY RECEIVED A TCASII RA TO CLB. ALREADY CLBING; THE LCL CTLR TOLD US TO MAKE A R 360 DEG TURN. WE FOLLOWED THE TCASII DIRECTIVE AND THE CONFLICT WAS RESOLVED. WE ALSO INITIATED THE R TURN. THE LCL CTLR THEN ADVISED US TO ENTER A R DOWNWIND FOR 8R AND FOLLOW A B-737 ON APCH TO 8R. THE SUBSEQUENT APCH AND LNDG WERE UNEVENTFUL. AT THE TIME OF THE RA; OUR LATERAL SEPARATION WAS 0 AND VERT SEPARATION WAS APPROX 200 FT. AFTER LNDG; I CALLED THE ATC FACILITY BY TELEPHONE AND SPOKE WITH SUPVR. AMONG OTHER THINGS; HE INDICATED THAT; AT THE TIME OF THIS INCIDENT; RWY 8L WAS TEMPORARILY CLOSED FOR SNOW REMOVAL; EVEN THOUGH THE APCH CTLR ADVISED US REPEATEDLY THAT THE OTHER ACFT WAS PROCEEDING TO THAT RWY. HE TRIED TO MINIMIZE THE MAGNITUDE OF THIS OCCURRENCE AND WAS SURPRISED THAT EVASIVE ACTION WAS INITIATED BY THE FLC; NOT ATC.