CPR JET REDUCED CLB RATE WHILE IN CLB FROM 5000 FT TO 8000 FT AFTER RECEIVING A TCASII RA ON APPARENT VFR TFC. RPTR SIGHTED TFC AND PASSED UNDER IT.

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WE HAD JUST DEPARTED PTK ARPT FOR ROC AND WERE BEING VECTORED FOR CLB BY DTW DEP. WE WERE ON AN EASTERLY ASSIGNED HDG AT 5000 FT. A CLB WAS ISSUED TO 8000 FT AND WE INITIATED THE CLB. AFTER WE HAD INITIATED THE CLB; DEP ISSUED US OPPOSITE DIRECTION TFC WHICH I BELIEVE WAS AT 6000 FT. A TA WAS ALSO ISSUED BY OUR TCASII AT ABOUT THIS SAME TIME; FOLLOWED WITHIN A FEW SECONDS BY AN RA TO REDUCE OUR CLB RATE. WE VISUALLY SPOTTED THIS TFC AT ABOUT THIS SAME TIME 2-3 MI AHEAD; JUST ABOVE OUR ALT (A SINGLE ENG PLANE). WITH OUR REDUCED CLB RATE; THE TFC PASSED DIRECTLY ABOVE US WITH THE TCASII SHOWING 400 FT SEPARATION. IT WOULD SEEM THAT ATC IMPROPERLY ISSUED US A CLB CLRNC WITH THIS TFC IN FRONT OF US. HAD WE NOT HAD THE TCASII SYS TO ALERT US; THE SIT COULD HAVE BEEN MUCH MORE SERIOUS AS WE DIDN'T HAVE TO MAKE ANY VIOLENT MANEUVERS TO AVOID THE TFC. IT APPEARED THAT ATC LOST SIGHT MOMENTARILY THAT THIS TFC WAS IN CONFLICT WITH US WITH THE ISSUANCE OF A FURTHER CLB AND WAS VERY MATTER OF FACT ABOUT CALLING THE TFC TO US AS WE WERE CLBING.