UPON RETURNING TO CVG; DUE TO ANTI-ICE DUCT WARNING ALARM; CL65 FLC LAND WITHOUT OBTAINING LNDG CLRNC.

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WE LANDED IN CVG ON RWY 36R WITHOUT CLRNC FROM THE TWR; INADVERTENTLY. WE HAD TO RETURN TO CVG FOR A NUISANCE WARNING MESSAGE (TRIPLE CHIME; AURAL WARNING 'ANTI ICE DUCT') THAT WOULD NOT GO AWAY. WE WERE GOING TO LAND CLOSE TO OUR MAX LNDG WT; PERHAPS OVERWT. I WAS THE PNF; THE FO WAS THE PF. DURING APCH AND JUST OUTSIDE THE FINAL APCH FIX; APCH TOLD US TO SLOW AS BEST WE COULD TO ALLOW FOR A DEP. WE SLOWED AS REQUESTED. INSIDE THE FAF; WE AGAIN REVIEWED THAT WE WERE GOING TO POSSIBLY LAND OVERWT AND TO KEEP THE VSI LESS THAN 300 FPM; AND THAT I WOULD CALL OUT THE VSI AS WE WERE TOUCHING DOWN TO HELP. ONCE AGAIN; WE RECEIVED THE TRIPLE CHIME; AURAL WARNING 'ANTI ICE DUCT' WARNING MESSAGE. OUR FOCUS WAS OBVIOUSLY SHIFTED FROM DOING THE TASK AT HAND TO SILENCING THIS NUISANCE MESSAGE. IT DISTR US. THE DISTR WAS SUCH THAT NEITHER MYSELF NOR THE FO RECALL APCH HANDING US OFF TO TWR. AS A MATTER OF FACT; WE BOTH SWEAR IT NEVER HAPPENED (WHICH IS NOT AN EXCUSE; BUT SHOWS WE WERE DISTR). THE FO CALLED FOR THE BEFORE LNDG CHK; I PERFORMED IT AS USUAL; BUT RECALL AFTER THE FACT THAT I NEVER SAID 'CLRED TO LAND.' I USUALLY FLIP THE 'RECOG LIGHT' SWITCH AS A REMINDER THAT WE'RE CLRED TO LAND (AS DOES 98% OF US AT THIS AIRLINE). AFTER TOUCHDOWN; APCH TOLD US TO CONTACT TWR ON 118.97; WHICH I DID. IMMEDIATELY; WE KNEW WHAT HAD HAPPENED. I WAS THEN INSTRUCTED TO CALL THE TWR WHEN WE GOT IN. WE TAXIED TO THE GATE UNEVENTFULLY; AND BOTH THE FO AND I REALIZED WE WERE SO WRAPPED UP IN THIS NUISANCE AURAL MESSAGE; WE BOTH NEGLECTED TO FULFILL OUR DUTIES AS CREW MEMBERS AND TO KEEP EACH OTHER OUT OF TROUBLE. I CALLED THE TWR; AND THEY CHASTISED ME (AS THEY HAD EVERY RIGHT TO); AND TOLD ME 'NO HARM; NO FOUL.' I WAS EXTREMELY EMBARRASSED I HAD DONE THIS. OUR PERFORMANCE WAS DEGRADED DUE TO THE FACT THAT WE LET THE NUISANCE WARNING MESSAGE DETRACT US FROM OUR DUTIES. IT HAPPENED SO EASILY. I WAS ALWAYS ONE TO THINK THIS WOULD NEVER HAPPEN TO ME; AND IT DID. IT IS EXTREMELY IMPORTANT TO STAY FOCUSED ON THE TASK AT HAND -- FLYING THE PLANE AND PUTTING ALL DISTRS OUT OF THE WAY. WE BOTH LEARNED A VALUABLE LESSON AND WILL BE EVER VIGILANT TO NEVER LET THIS HAPPEN AGAIN. I WOULD LIKE TO ADD THAT THE WARNING MESSAGE CAME ON CONTINUALLY FOR ABOUT 15-20 MINS; AND SEVERAL TIMES DURING OUR APCH.