MDT HAS TCASII RA AND VECTOR FROM CTLR; DOES NOT COMPLY WITH EITHER.

Narrative

WE WERE AT 5000 FT AND AN ASSIGNED HDG. THE TCASII WENT OFF ALERTING US OF TFC AT OUR 10 O'CLOCK POS. ABOUT THE SAME TIME; ATC CALLED ABOUT THE TFC. HE WAS ABOUT 500 FT ABOVE US AND 2 NM AWAY. I LOOKED UP AND SPOTTED A SMALL METALLIC BALLOON. I FOCUSED ON THE BALLOON AND DID NOT SPOT THE TFC. MY FO SAID HE HAD THE TFC IN SIGHT. ATC WAS ASKING IF WE HAD THE TFC. I WAS HESITANT ABOUT CALLING OUT THE TFC BECAUSE I DID NOT SEE HIM. FINALLY; THE TCASII TOLD US TO DSND AND AT THE SAME TIME ATC WAS TELLING TO TURN TO A HDG THAT WOULD PARALLEL THE TFC. I SAID WE HAD THE TFC AND STARTED TO CLB. I TOLD ATC WE WERE CLBING TO AVOID THE CONFLICT. WE THEN CLBED UP TO 5500 FT. DURING THIS PERIOD; THE TFC STARTED TO DSND TO OUR ASSIGNED ALT. I MOMENTARILY CAUGHT A GLIMPSE OF THE TFC AS HE WAS PASSING OUR NOSE. MY FO SAW THE ACFT DSNDING VISUALLY AND HAD STARTED TO CLB BEFORE THE TCASII TOLD US TO DSND. WE THEN DEVIATED FROM OUR ASSIGNED ALT OF 5000 FT MSL UP TO 5500 FT MSL TO AVOID THE CONFLICT.THE OTHER ACFT DID LEVEL-OFF AT 5000 FT MSL. BECAUSE WE WERE IN THE CLB; MY FO DECIDED THAT IT WOULD NOT BE A GOOD IDEA TO DSND. ALSO; WHEN ATC GAVE US A HDG; TURNING WOULD HAVE PUT US BELLY-UP TO THE ACFT AND WE WOULD HAVE LOST IT VISUALLY. PLUS; THE ACFT WAS WITHIN A MI OF US BY THEN; AND WE WOULD NOT HAVE BEEN ABLE TO TURN IN TIME TO AVOID THE CONFLICT. THE OTHER ACFT WAS A MOONEY; AND WE DID NOT GET AN AMPLE WARNING FROM ATC OR THE TCASII TO AVOID THE SIT ENTIRELY.