AN ALLEGED LOSS OF SEPARATION RPTED BY DEP CTL TO A DEP FOKKER 70 FLYING AN INCORRECT HDG AFTER DEP DTW; MI.

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I WAS THE CAPT (PNF) ON OUR COMPANY FLT FROM DETROIT METRO ARPT TO CINCINNATI LUNKEN ARPT. THE FO (PF) WAS IN THE L SEAT. WE RECEIVED AN ATC CLRNC TO 'TAXI INTO POS AND HOLD ON RWY 21R;' AND WERE TO EXPECT TO HOLD IN POS WHILE TWR DEPARTED AN ACFT OFF A PARALLEL RWY ON THE W SIDE OF THE ARPT. WHEN OUR TKOF CLRNC WAS ISSUED; IT INCLUDED A HDG TO FLY AFTER DEP; WHICH I ENTERED INTO THE FLT MODE PANEL. ONCE AIRBORNE AND CLBING THROUGH 400 FT AGL; THE PF CALLED FOR THE HDG SELECT TO BE ACTIVATED AND I CONTACTED DEP WHILE HE FLEW THE COMPANY CLB PROFILE. AFTER WHAT SEEMED TO BE A COUPLE OF MINS; DEP ASKED OUR HDG; WHICH I REPLIED 220 DEGS. AGAIN; MAYBE 1 MIN PASSED WHEN THE CTLR ISSUED A NEW HDG -- 200 DEGS. WE FLEW THAT HDG FOR A SHORT TIME; THEN WE WERE CLRED TO OUR FIRST FIX (CAVVS). ALL FURTHER CONTACT WITH DEP WAS ROUTINE; ENDING WITH OUR HDOF TO ZOB. I DIDN'T KNOW OF ANY ERRORS OR CONFLICTS UNTIL DAYTON APCH RELAYED A MESSAGE FROM DETROIT TO CALL BECAUSE OF 'LOSS OF SEPARATION' PROB. IN MY CONVERSATION WITH DETROIT METRO TWR; I WAS TOLD THAT THE HDG ISSUED BY TWR WAS 200 DEGS; AND THAT I READ BACK 200 DEGS TO THEM WHEN I READ BACK MY TKOF CLRNC. ON OUR INITIAL CLB OUT OF DETROIT; I DID SEE THE ACFT THAT DELAYED OUR DEP; I BELIEVE IT WAS AN AIRBUS 320; AND IT WAS AT OUR 1 O'CLOCK POS; HIGHER AND SEVERAL MI AHEAD. WHEN I LOOKED AT OUR TCASII; I BELIEVE IT WAS INDICATING ABOUT 1000 FT ABOVE US; AND MAYBE 5 MI AHEAD; ON OUR NAV DISPLAY; IT WAS INDICATED AS A HOLLOW BLUE DIAMOND. IN HINDSIGHT; WE DID NOT PRACTICE GOOD CRM. PER OUR COMPANY POLICY; I SET THE FLT MODE PANEL IN ACCORDANCE TO OUR SOP; BUT THE FO NEVER CONFIRMED IT NOR REFED THE HDG WHEN ASKING FOR THE HDG SELECT TO BE ENGAGED AFTER TKOF. WHEN DEP QUERIED US ABOUT OUR ASSIGNED HDG; AND I RESPONDED 220 DEGS; I ASKED THE FO IF I MAY HAVE ENTERED IN THE WRONG HDG PRIOR TO DEP; BUT HE REASSURED ME THAT 220 WAS THE CORRECT HDG ASSIGNMENT. I'VE NEVER BEEN AFRAID TO ASK ATC TO REPEAT A CLRNC IF ONE OF US IN THE COCKPIT WAS UNSURE OF THE INSTRUCTIONS; BUT FOR THAT TO BE AN EFFECTIVE DETERRENT FOR PREVENTING SOMETHING LIKE THIS FROM HAPPENING AGAIN; BOTH PLTS NEED TO BE ENGAGED IN ACTIVE LISTENING.