CRJ700 FLT CREW HAS TO TAKE EVASIVE ACTION DURING DSCNT. ZKC CTLR ISSUES ALERT AND A REVISED CLRNC.

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WAS GIVEN PLT DISCRETION TO DSND TO FL240. INITIATED DSCNT. AFTER HAVING DONE THIS ATC CALLED TO MAINTAIN FL370. THE DSCNT WAS ARRESTED AND SECONDS AFTER WE GOT THE TFC ON TCAS; ATC INSTRUCTED TO TURN TO A HDG OF 180 DEGS. WE INITIATED THE TURN; BUT HAD TO DISCONNECT THE AUTOPLT TO INCREASE THE RATE OF TURN TO THE ASSIGNED HDG. THE OTHER ACFT WAS INSTRUCTED TO TURN IN OPPOSITE HDG. THE MANEUVER WAS MODERATELY AGGRESSIVE TO ENSURE A SAFE EVASION. WE DID NOT SEE THE OTHER ACFT DUE TO THE TURN; BUT FROM TCAS INTERP IT WAS CLOSE; APPROX 2000-3000 FT HORIZ AND -200 FT TO -100 FT VERTLY. AFTER THE XING WE CONTINUED DSCNT AND WAS INSTRUCTED TO FLY DIRECT TO TRAKE AGAIN. THE CTLR DID APOLOGIZE TO US AND TO THE OTHER ACFT AND ACKNOWLEDGE THAT IT WAS HIS MISTAKE. THE WORSE SCENARIO WAS AVOIDED DUE TO THE CORRECTIVE TURN AND NOT CHANGES IN ALT. THE CTLR KEPT ASKING US TO CONFIRM IF WE WERE THROUGH FL350 IN A VERY CONCERNED TONE OF VOICE. WE COULD NOT REPLY IMMEDIATELY SINCE WE WERE TAKING EVASIVE ACTION.