SHORTLY AFTER TKOF AT BKL; AN H25 CREW HAD A CLOSE ENCOUNTER WITH A C172 REQUIRING A 60 DEG BANK TO MISS THE ACFT.

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WE WERE CLRED FOR TKOF ON RWY 6R AT BKL. OUR CLRNC WAS 'TURN L HDG 350 DEGS; MAINTAIN 2000 FT MSL.' AT 400 FT AGL; THE CAPT CALLED VF TO SPD AND FLAPS UP. I SELECTED THE FLAPS UP. THE CAPT STARTED A L TURN IN ABOUT 20 DEGS OF BANK TO 350 DEGS. THE TCASII UNIT SAID 'TFC; TFC.' I LOCATED THE C172 AT 11:30 O'CLOCK POS AND 400 FT ABOVE US. THE CAPT IN THE L TURN COULD NOT SEE THE TFC. BASED ON OUR CLOSURE RATE AND RATE OF TURN; IT WAS CLR TO ME THAT WE COULD HIT THE CESSNA. I TOOK CTL AND ROLLED THE ACFT INTO A 60 DEG L BANK UNTIL CLR OF THE TFC. WE CLRED THE TFC BY 1/2 MI AT 1400 FT MSL. THE CESSNA WAS INSTRUCTED TO RPT 2 MI E OF RWY 6R TO THE TWR. HE NEVER MADE THE RPT. THE CTLR DID NOT ADVISE US OF THE CESSNA PRIOR TO OUR DEP. THE GPWS ALERTED 'BANK ANGLE' AND 'DON'T SINK.' THE TCASII UNIT MOMENTARILY LOST THE CESSNA IN THE TURN; BUT ONCE LEVEL AND BEHIND US; ALERTED 'TFC; TFC' AGAIN. WE WERE INSTRUCTED TO CONTACT DEP CTL. I RPTED THE NMAC TO LAKEFRONT TWR. SUPPLEMENTAL INFO FROM ACN 551227: WE WERE JUST STARTING OUR TURN WHEN THE TCASII ACTIVATED; 'TFC; TFC.' I YELLED TO THE FO 'WHERE IS HE?' HE SAID HE HAD HIM; 'HE'S CLOSE; TIGHTEN UP THE TURN.' THE FO THEN SAID 'THAT'S NOT ENOUGH.' I SAID; 'I STILL DON'T SEE HIM;' AS THE HAZE WAS VERY THICK OVER THE WATER. HE THEN TOOK THE AIRPLANES AND ROLLED INTO A LITTLE OVER 45 DEGS OF BANK AND EVADED THE OTHER ACFT. IT WAS HARD TO TELL HOW FAR WE PASSED APART; BUT THE SO STATED SOMEWHERE BTWN 1/2 - 1 MI. UPON LNDG AT CMH; I CONTACTED THE TWR MGR AT BKL FOR AN EXPLANATION. HE SAID THE SAME CTLR PREVIOUSLY MENTIONED HAD AN INBOUND CESSNA FROM THE E THAT WAS TO RPT 2 MI E. OBVIOUSLY THEY LOST TRACK OF HIM AND HE WAS JUT STARTING TO ENTER THE PATTERN ON A L DOWNWIND. WE WERE NOT GIVEN ANY TA'S AT ALL; AND WERE GIVEN A CLBING L TURN THAT PUT US ON A DIRECT COURSE WITH THE CESSNA. CALLBACK CONVERSATION WITH RPTR ACN 551462 REVEALED THE FOLLOWING INFO: RPTR RECAPPED MOSTLY WHAT WAS CONTAINED IN HIS RPT. HE STRONGLY FEELS THE CTLR SHOULD HAVE ISSUED A TA. HE APPARENTLY DID NOT KNOW THAT IT IS THE PLT'S RESPONSIBILITY TO RPT AN NMAC AND ADVISE ATC HE WISHED TO FILE A RPT.