DO328 CREW HAD A TCASII RA IN ZOB CLASS A AIRSPACE.

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FLYING AS ACR X FROM FWA TO PIT IN CRUISE AT FL230 (OR FL210) IN IMC AT XA30 EST; WAS CLRED DIRECT (VIA FMS) TO CUTTA INTXN (APPROX 75 NM COURSE APPROX 070 DEGS). AUTOPLT/FLT DIRECTOR WAS ON. CAPT WAS PF. RECEIVED A TA FOR A TARGET APPROX 5 NM AT APPROX 2 O'CLOCK POS; 400 FT ABOVE US. SHORTLY THEREAFTER (APPROX 5 SECONDS) FOLLOWED AN RA TO DSND. PF DISCONNECTED AUTOPLT AND INITIATED DSCNT (PER COMPANY POLICY). SIMULTANEOUSLY; I RPTED DSCNT TO ATC. ATC RESPONDED THAT TFC WAS AT 2 O'CLOCK (MAY HAVE SAID 1 O'CLOCK); 1000 FT BELOW US WITH NO OTHER TFC AROUND. RA STOPPED AND PF STOPPED DSCNT APPROX 400 FT BELOW ASSIGNED ALT; AND CLBED BACK UP TO ORIGINAL ALT. ATC RPTED THAT SEPARATION WITH OTHER ACFT HAD BEEN LOST APPROX 600 FT VERT AND 3.1 (OR 2.1) NM LATERAL. FLT PROCEEDED NORMALLY TO PIT WHERE PF NOTIFIED MAINT THAT TCASII UNIT WAS MALFUNCTIONING. MAINT TESTED TCASII; OPS CHKED GOOD AND ACFT WAS PLACED BACK IN SVC. DURING RA; RED INTRUDER SYMBOL WAS DISPLAYED ALONG WITH SOLID BLUE TFC SYMBOL. I MENTIONED TO ATC THAT POSSIBLY IT WAS A SECONDARY RETURN FROM THE SAME ACFT AND MAYBE ITS XPONDER WAS MALFUNCTIONING. ATC RESPONDED THAT THEY OBSERVED ONLY 1 TARGET. PF LATER MENTIONED THAT NO INDICATION OF DSCNT APPEARED ON VSI WHICH IS AN INDICATION THAT OUR TCASII UNIT MAY HAVE MALFUNCTIONED. I BELIEVE OUR TCASII MALFUNCTIONED CAUSING US TO DSND TOWARDS ANOTHER ACFT.