RPTED LOSS OF SEPARATION BTWN DSNDING ACR B727 AND A CLBING ACR B767.

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WHILE APCHING CINCINNATI ARPT FOR A LNDG ON RWY 36R; WE WERE INSTRUCTED BY CVG APCH CTL TO DSND FROM 6000 FT TO 5000 FT AND TURN TO A HDG OF 340 DEGS TO INTERCEPT THE CVG RWY 36R LOC. DURING THE TURN AND DSCNT WE RECEIVED A TCASII TA; FOLLOWED BY A TCASII RA. THE RA ADVISED AN IMMEDIATE 2500 FPM RATE OF CLB ON THE TA VSI. THE PF; ME; HAD A POSITIVE VISUAL ON THE CONFLICTING TFC. IT APPEARED THAT THE B767 WAS CLBING AND TURNING INTO US. MY VISUAL INSTINCT WAS TO TURN AWAY AND DSND; THUS KEEPING THE ACFT IN SIGHT. HOWEVER; WE FOLLOWED THE TCASII ADVISORY AND CLBED AND TURNED AGGRESSIVELY. ATC WAS ADVISED THAT WE WERE TAKING EVASIVE MANEUVERS. THERE SEEMED TO BE A LONG PAUSE BEFORE ANY ACKNOWLEDGMENT WAS GIVEN. WE WERE ATTEMPTING TO RETURN TO 5000 FT WHEN WE WERE TOLD TO CLB TO 6000 FT AND TURN TO 090 DEGS. DURING THIS MANEUVER WE RECEIVED AN ADDITIONAL TCASII TA TO MONITOR VERT SPD. THIS EVENT ENDED QUICKLY. REMAINDER OF APCH AND LNDG WAS UNEVENTFUL. APCH CTL SUPVR; AFTER CONTACT; STATED THIS WAS AN ERROR BY APCH CTL. SUPPLEMENTAL INFO FROM ACN 391578: WE AGGRESSIVELY CLBED ACCORDING TO THE TCASII COMMAND AND AVOIDED THE OTHER JET.