LGT ON INITIAL CLB HAS TCASII RA. RESPONDS WITH DSCNT.

Narrative

MSP TWR CLRED AN LTT FOR TKOF. TWR THEN CLRED MY ACFT INTO POS TO HOLD. AFTER LINING UP ON THE RWY; TWR CLRED BY ACFT FOR TKOF TO MAINTAIN RWY HDG; EXPECT A TURN AT THE FIELD BOUNDARY. AFTER TKOF A TURN WAS NOT GIVEN AND I CONTINUED ON MY RWY HDG WITH E LTT IN SIGHT. AT APPROX 2500 FT TWR GAVE ME A TURN TO 320 DEG. THE FO ACKNOWLEDGED AND SET 320 DEG ON THE HDG SELECT. I STARTED THE TURN AND NOTED THAT THE LTT WAS ALSO TURNING R AT THIS TIME. AT 4000 FT THE TCASII GAVE A TA. I WAS REDUCING MY RATE OF CLB AT THIS TIME. AT 4500 FT THE TCASII GAVE A TFC RESOLUTION AND I STARTED A DSCNT AS ADVISED BY THE TCASII; ON A HDG OF 32 DEG AND APPROX 4400 FT. THE LTT PASSED OVER THE TOP OF MY ACFT. I CAN ONLY ASSUME THE LTT WAS AT 5000 FT WHICH IS THE ALT RESTRICTION ON THE DEP FOR MSP. DEP CTL CALLED AND ASKED IF MY ACFT HAD BEEN GIVEN A 360 HDG BY MSP TWR AND MY FO RESPONDED NEGATIVE; WE WERE GIVEN A 320 DEG HDG. DEP THEN ISSUED A 360 DEG HDG AND I REFUSED AS THE LTT HAD JUST PASSED OVERHEAD; AND I DID NOT KNOW WHERE HE WAS. DEP CTL THEN CLRED MY ACFT TO 4000 FT TO MAINTAIN AND TURN R TO 360 DEG. I THEN COMPLIED WITH THESE INSTRUCTIONS. I WAS AT APPROX 4200 FT WHEN THOSE INSTRUCTIONS WERE ISSUED. I ASKED MY FO TO ADVISE DEP CTL THAT WE HAD FOLLOWED A CONFLICT RESOLUTION AND THEY ACKNOWLEDGED AND ALSO ADVISED US THAT THEY WERE CHKING WITH THE TWR ABOUT WHAT HDGS WERE ISSUED. I FEEL THAT THE TWR CTLR WAS NOT TOTALLY AWARE OF THE DIFFERING SPDS OF THE 2 ACFT; AND HE SHOULD HAVE ISSUED THE LTT A 320 DEG HDG AND MY ACFT A 360 DEG HDG SO THAT MY ACFT WOULD TURN INSIDE THE LTT AND MAINTAIN PROPER SPACING.