A CPR LTT CREW RPTS THAT THEY HAVE DOUBTS ABOUT TFC THAT CAUSED A TCASII RA.

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WHILE IN CRUISE FLT AT 11000 FT JUST NO OF THE DQO VOR (V433) IN IMC; ATC ADVISED ME THAT WE HAD TFC BELOW CLBING TO 10000 FT. ATC FURTHER INDICATED THAT HE WAS NOT TALKING WITH THE ACFT AND ASSUMED THAT THIS ACFT WAS GOING TO STOP HIS CLB AT 10000 FT. A FEW MOMENTS AFTER RECEIVING THIS XMISSION WE HAD A TA ON OUR TCASII WHICH SHOWED A TARGET AT THE 2-3 O'CLOCK POS AND 1700 FT BELOW OUR ALT. WHAT SEEMED TO BE ONLY A FEW SECONDS LATER; WE EXPERIENCED AN RA WITH INSTRUCTIONS TO 'CLB; CLB; CLB;' IMMEDIATELY FOLLOWED BY 'INCREASE CLB.' THE 'INCREASE CLB' MODE ON OUR TCASII COMMANDS A MINIMUM CLB SPD OF 2500-3000 FPM. AT APPROX 13200-13400 FT THE TCASII GAVE THE 'CLR OF CONFLICT' COMMAND AT WHICH TIME I BEGAN A DSCNT BACK TO 11000 FT. TO THIS DAY; I DO NOT KNOW WHAT CAUSED THE PROB. HOWEVER; IF IT WAS A FALSE SIGNAL RECEIVED BY THE TCASII OR SOME TYPE OF TCASII FAULT; THEN FIXES TO THE TCASII SYS MUST BE COMPLETED ASAP BEFORE MAJOR MIDAIR COLLISIONS OCCUR. SUPPLEMENTAL INFO FROM ACN 257190: WE'RE CLBING AT SOMETHING OVER 3000 FPM LOOKING AT EACH OTHER; WONDERING WHY WE'RE GETTING SUCH A WARNING ON TFC AT SUCH A DISTANCE. AT 13100 FT WE GOT THE 'CLR OF CONFLICT' COMMAND. OUR CLB PEAKED AT 13400 FT. WE ADVISED ATC AND WENT BACK DOWN TO 11000 FT. ATC ASKED WHAT OUR TCASII HAD DISPLAYED. WE TOLD HIM THAT FOR THE DURATION OF THE ENTIRE INCIDENT WE HAD ONLY THAT 1 TARGET DISPLAYED AT 3 O'CLOCK. IN MY OPINION THE ONLY BAD ELEMENT OF THE ENTIRE SIT WAS CREATED BY THE TCASII.