CVG CTLR EXPERIENCED LOSS OF SEPARATION BTWN ARR AND DEP ACFT WHEN INTRAFAC COORD WAS INCOMPLETE AND UNCLR AS TO WHICH CTLR WAS RESPONSIBLE FOR WHAT TYPE OF SPACING CTL.

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CINCINNATI WAS IFR WITH FREEZING CONDITIONS. RWYS WERE BEING DEICED AND PIREPS FOR BRAKING ACTIONS WERE BEING SOLICITED. FREIGHT B727 INBOUND FROM FLM VOR REQUESTED RWY 27; THOUGH WE WERE LNDG RWYS 18L/R. ARR CTLR WAS VECTORING B727 FOR A DOWNWIND TO RWY 27 AND HAD COORDINATED THIS WITH ME (DEP CTLR). A DEP CAME OFF RWY 18L. JS32 WAS TOLD TO CLB AND MAINTAIN 8000 FT 'TWICE' AND TURNED TO A HDG OF 090 DEGS (AGAIN HAD TO BE TOLD TWICE). WITH OTHER SMALLER ACFT IN MY AIRSPACE AT 5000 FT; 6000 FT; AND 7000 FT; I WAS CLBING THE JS32 TO TOP THIS TFC. THE ARR CTLR; HAVING COORD WITH ONE PRECEDED; TO DSND THE B727 TO 7000 FT. WHEN I SAW THE B727 DSNDING; I IMMEDIATELY TOLD THE JS32 TO TURN R HDG 180 DEGS; POINTED OUT TFC AND WHEN HE RESPONDED THAT HE DIDN'T HAVE THE TFC IN SIGHT; I TOLD HIM TO TURN IMMEDIATELY HDG 180 DEGS. HE FINALLY TURNED WHEN HE GOT AN RA ALERT. WHILE THE PROBS THAT OCCURRED WERE MY ASSUMPTION THAT THE ARR CTLR WAS GOING TO STAY AT 9000 FT (WHICH I DIDN'T ENSURE). I FEEL THIS COULD HAVE HAD A BETTER OUTCOME IF I HADN'T HAD TO REPEAT MYSELF (MY XMISSION) TO THE PLT OF THE JS32. AS A CTLR; IT IS VERY FRUSTRATING WHEN YOU ARE BUSY OR WEATHER IS BAD; TO HAVE TO MAKE ALL YOUR XMISSIONS 2 OR 3 TIMES TO EVERY PLANE. THIS HAPPENS FREQUENTLY AND WHILE I KNOW PLTS HAVE A LOT TO ACCOMPLISH IN THE COCKPIT; IT SEEMS ONLY LOGICAL TO ME THAT THE CLOSER YOU GET TO YOUR DEST; THE MORE VIGILANT YOU SHOULD BE IN STAYING ALERT. THE CLOSER YOU ARE TO THE ARPT THE MORE TFC THERE IS AND THE MORE VITAL IT IS FOR YOU TO ACT ON ATC'S INSTRUCTIONS WITH AS LITTLE HESITATION AS POSSIBLE.