RPTR IS NOT SURE HE DSNDED IN ACCORDANCE WITH THE CTLR INSTRUCTIONS BECAUSE THE CTLR TOLD HIM TO CLB BACK TO THE ALT HE HAD JUST DSNDED THROUGH AND TCASII TA OCCURRED.

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ON A FLT FROM MDW TO DTW; AS WE WERE APCHING LITCHFIELD; WE WERE GIVEN A SHORTCUT TO DEPART LITCHFIELD ON THE 116 DEG RADIAL FOR THE 35 DME FIX; MIZAR. AT THAT TIME WE HAD ALREADY BEEN GIVEN DISCRETION TO 16000 FT. WE STARTED OUR DSCNT; ANTICIPATING THE 12000 FT XING RESTR AT MIZAR AS DEPICTED ON THE STAR. DURING THE DSCNT; WE WERE GIVEN THE DSCNT WHICH WE UNDERSTOOD TO BE 'CROSS MIZAR AT 11000 FT AT 250 KTS.' WHEN WE REACHED 11000 FT; WE WERE TOLD TO LEVEL AT 12000 FT. WE INDICATED WE WOULD NEED TO CLB BACK TO 12000 FT; WHICH WE DID. AT THE TIME WE WERE TOLD TO LEVEL AT 12000 FT (WHEN WE WERE AT 11300 FT) I NOTICED A THREAT APPEAR ON TCASII WITHIN THE THREAT CIRCLE (15 MI RANGE) AND 1400 FT LOWER THAN US. AT THE TIME WE WERE TOLD TO CLB; WE HEARD ANOTHER ACFT ISSUED A TURN; AND WE IN TURN WERE GIVEN A TURN. I DO NOT KNOW IF THERE WAS A POTENTIAL CONFLICT; OR IF IT WAS JUST A COINCIDENCE. NO OTHER CTLR REMARKS WERE MADE PRIOR TO US BEING TURNED OVER TO DTW APCH. AS CAPT; I WAS FLYING; AND I DO NOT BELIEVE THERE WAS A CONFLICT.