DO328 LNDG COS HAS TCASII TA AND TCASII RA WITH C337 ON APCH.

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WE WERE ON RWY 17L LOC AND GS AND CLRED FOR A VISUAL APCH WITH COS TRACON. ATC ADVISED US OF A CESSNA SKYMASTER AT A 10 O'CLOCK POS TFC WHICH WOULD BE VECTORED BEHIND US TO RWY 17R AND ADVISED US TO CONTACT TWR. WE WERE NOW APCHING ABOUT 9000 FT MSL AND 200 KIAS WITH FLAPS AND GEAR UP AS I RECALL. WE WERE BOTH LOOKING FOR THE TFC; I SWITCHED TO THE TWR FREQ; BUT DIDN'T CALL BECAUSE WE WERE BOTH ALERTED BY A TCASII TA. WE HAD SEEN THE TFC ON THE TCASII BEFORE; BUT NOW; IT WAS INSIDE OF 2.5 MI AND 100-300 FT BELOW US. WE RECEIVED A TCASII RA JUST A MOMENT AFTER THE INITIAL TA TO CLB. THE CAPT ADDED A LOT OF PWR AND AGGRESSIVELY INITIATED A PITCH-UP INTO A STEEP CLB. NEITHER OF US HAD GOTTEN THE SKYMASTER IN SIGHT. WHEN WE INITIATED THE RA MANEUVER; THE TFC WAS AT OUR ALT AND LESS THAN A MI AS ON THE TCASII DISPLAY. CAPT SAID HE NOW SIGHTED THE PLANE IN A L BANK POINTED TOWARD US AT OUR 10 O'CLOCK POS; 1/8 MI; AND 200 FT BELOW US AS WELL AS ON THE TCASII. I CONTACTED TWR AND ADVISED WE HAD EXECUTED A TCASII RA. TWR SAID THE OTHER ACFT HAD US IN VISUAL CONTACT; WE DOUBT IT. A PAX ON THE GND ASKED IF THE TWR TOLD US ABOUT THE OTHER PLANE. THIS WAS AN ENTIRELY UNACCEPTABLE LOSS OF SEPARATION; IT SEEMED TO ME THE CESSNA WASN'T GIVEN A VECTOR (HEADING) AS WE HAD BEEN TOLD BECAUSE IF SO THAT WOULD'VE BEEN AN ATC BUST. IF HE ACTUALLY HAD VISUAL CONTACT WITH US; HE WAS STILL WAY TOO CLOSE.