ZKC ARTCC RADAR CTLR INADVERTENTLY DSNDS A CARGO ACR TO FL230 RESULTING IN A CONFLICT WITH A KING AIR.

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WE WERE HANDED OFF TO THE NEXT SECTOR CTLR WHO GAVE US A CLRNC TO CROSS 85 W OF VHP (BRICKYARD VOR) AT FL230. I COPIED THIS ON MY NOTE PAD AND READ IT BACK. MY COPLT STARTED COMPUTING HIS DSCNT SO AS TO LOOSE 6000 FT (WE WERE AT FL290); AND MAKE THE XING RESTR. WE RPTED TO ZKC THAT WE WERE DSNDING. AS WE REACHED FL230 WE WERE HANDED OFF TO ZID. I CHKED IN AT FL230. INDY RESPONDED 'VERIFY YOU'RE AT FL240.' I REPLIED 'NEGATIVE; WE'RE AT FL230.' 'OUR CLRNC WAS TO CROSS 85 W OF VHP AT 230.' EVIDENTLY; CTR THOUGHT I HAD FINISHED MY XMISSION WHEN I SAID 'FL230;' AND MADE A XMISSION TO ANOTHER ACFT. WHEN I RELEASED MY MIKE BUTTON; I HEARD CTR SAY 'DSND TO 11000 FT.' I ACKNOWLEDGED HIS INSTRUCTION 'RODGER ACR X; DSND TO 11000 FT.' HE THEN CAME BACK 'NEGATIVE ACR X; CLB TO FL240;' AND THEN RE-ISSUED HIS CLRNC TO ANOTHER ACFT TO DSND TO 11000 FT. WE CLBED TO FL240. APPROX 15 MINS LATER; THE CTLR DSNDED US FOR ARR AT IND. AS HE TURNED US OVER TO INDY APCH CTL; HE XMITTED A TELEPHONE NUMBER AND ASKED THAT THE CAPT CALL ZID DUE TO A POSSIBLE ALT DEV AND TFC CONFLICT. I CALLED THE CTR AND SPOKE WITH A SUPVR. HE INFORMED ME THERE HAD BEEN A TFC CONFLICT ALERT; AND AN INVESTIGATION HAD BEEN INITIATED. HE SAID KANSAS CITY LOW SECTOR HAD HANDED OFF A KING AIR AT FL230; WHO WAS ALSO EBOUND; AND HAD HANDED US OFF AT FL240. WHEN WE BOTH CHKED IN AT THE SAME ALT; A TFC ALERT SOUNDED. HE STATED ZKC HAD BEEN CONTACTED AND ASKED TO REVIEW THE TAPES. HE TOLD ME HE HAD NOT RECEIVED WORD OF THE TAPE CONTENTS. I GAVE HIM MY CELL-PHONE NUMBER AND ASKED HIM TO CALL ME AS SOON AS HE HAD THE RESULTS OF THE TAPES. APPROX 1 HR LATER; A QUALITY ASSURANCE CTLR CALLED AND SAID THE TAPES HAD BEEN REVIEWED AND THAT WE HAD BEEN CLRED TO FL230 AND INDICATED WE (THE FLT CREW) WERE OFF THE HOOK.