FLC OF F100 HAS NMAC WITH CESSNA WHEN 600 FT AIRBORNE ON TKOF. OPERROR.

Narrative

ATC FACILITY: TUL TWR. LOCATION: RWY 18L TUL. CLRED FOR TKOF ON RWY 18L; FO FLYING. AT 600 FT AGL; TFC CALLED AT 2 O'CLOCK. AT SAME TIME BOTH PLTS SAW THE HIGH WING CESSNA XING 100 OR 200 FT ABOVE R TO L. WE WERE ON RWY HDG. CONTINUING THAT HDG OR TURNING L; WE WOULD HAVE COLLIDED. WE INCREASED RATE OF CLB AND INITIATED A R TURN UNTIL CLR OF CONFLICT; THEN WENT BACK TO RWY HDG. THE TCASII GAVE US AN RA AT THE SAME TIME WE INITIATED OUR TURN. NO EVASIVE INSTRUCTIONS WERE GIVEN BY ATC. THE CAPT COMMENTED TO LCL ATC THAT WE WOULD HAVE TO RPT THAT. THE CESSNA ASKED IF HE HAD DONE SOMETHING WRONG. NO REPLY. WE WERE BOTH TOLD TO CONTACT DEP. THE DEP CTLR GAVE US THE PHONE NUMBER TO CALL. MY UNDERSTANDING IS THAT THE CAPT WAS TOLD THAT THE TWR CTLR HAD CLRED THE CESSNA FOR TKOF OF RWY 18R WITH A L TURN TO 090 DEGS; THEN CLRED US FOR TKOF ON RWY 18L. I THINK THE SEPARATE CLRNCS WERE ISSUED ON DIFFERENT FREQS BUT OUR SITUATIONAL AWARENESS MIGHT HAVE BEEN DECREASED BY A DISCUSSION ABOUT A MAINT SIGNOFF. THIS DISCUSSION TOOK PLACE WHILE HOLDING SHORT OF RWY WHICH IS WHEN THE TKOF CLRNC WAS ISSUED.