MD88 CREW; IN RESPONSE TO A LOW WING GA ACFT; HAD A TCASII RA IN CVG CLASS E AIRSPACE.

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ON CLBOUT PASSING 11000 FT WITH CLRNC TO FL230; WE INITIALLY OBSERVED A HOLLOW DIAMOND TARGET AT OUR 10 O'CLOCK POS SHOWING 1000 FT ABOVE US. AS WE CONTINUED OUR CLB; THE TARGET RAPIDLY BECAME A RED SQUARE AND WE RECEIVED THE REDUCE CLB; VERBAL WARNING. THE VSI DISPLAY SHOWED A RED BORDER FOR ALL CLBS AND A SMALL GREEN BORDER FOR A SLOW DSCNT. I REVERSED OUR CLB AND TOPPED OUT AT APPROX 12000 FT. THE TCASII SHOWED US LEVEL WITH THE TARGET MOMENTARILY. I WAS ABLE TO SPOT THE TARGET VISUALLY AT ABOUT THE TIME WE REVERSED OUR CLB. IT WAS A LOW WING SINGLE ENG GA ACFT. THE WX CONDITIONS WERE VERY HAZY ABOVE A BROKEN TO OVCST LAYER. MY FO NOTIFIED ATC THAT WE WERE COMPLYING WITH A TCASII DIRECTIVE AND WAS TOLD THAT THERE WAS NO TARGET; 'EXCEPT A VFR TARGET AT 12500 FT.' THE CTLR WAS MODERATELY BUSY; BUT HAD MADE NO ATTEMPT TO NOTIFY US OF THE TFC OR TO MODIFY OUR CLRNC. I WOULD GUESS THAT OUR NEAREST APCH TO THE OTHER ACFT WAS APPROX 1/2 MI AT CO-ALT. THE HAZARD HERE IS OBVIOUS; AND I QUESTION THE CTLR'S JUDGEMENT AND PROCEDURAL COMPLIANCE IN NOT CALLING THE TFC TO OUR ATTN OR MODIFYING OUR CLRNC.