CGA GETS A TCASII ON SHORT FINAL AND STARTS TO CLB; THEN CHANGES HIS MIND AND LANDS. TFC WAS A COPTER LOW.

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I WAS WORKING LCL CTL AT THAT MOMENT WORKING SEVERAL INBOUND ACFT. A HELI CHKED IN ON FREQ 4 MI SE OF ARPT VFR. I OBSERVED HIS TARGET ON THE BRITE SCOPE AS WELL AS THE TARGET OF CGA X (ON AN IFR FLT PLAN) INBOUND ABOUT 1 1/2 MI NE OF OBK. THE HELI WANTED TO GO NWBOUND FROM PRESENT POS. I INSTRUCTED HIM TO FLY E OF THE APCH COURSE OF RWY 16 DUE TO CGA X 1 1/2 NE OF OBK BEING VECTORED INBOUND FOR THE ILS RWY 16 APCH. HELI REQUESTED TO OVERFLY THE ARPT AND PROCEED NWBOUND TO HIS DEST. THE JET (CGA X) RPTED ON FREQ ON A 2 MI FINAL SO I GAVE HIM HIS LNDG CLRNC. WHILE THIS WAS ALL HAPPENING; THE HELI HAD OVERFLOWN THE ARPT AND WAS W OF THE APCH COURSE OF RWY 16 HEADED NWBOUND AT 1100 FT MSL. AS THE JET APCHED 1 MI FINAL THE PLT ADVISED ME THAT HE WAS GOING AROUND DUE TO 'TCASII RESOLUTION.' I LOOKED OUT THE WINDOW AND THE BRITE SCOPE AND THERE WAS ONLY 1 OTHER TARGET IN HIS AREA; THE HELI ABOUT A MILE W OF HIS POS GOING THE OPPOSITE DIRECTION (NWBOUND) AT 1100 FT MSL. I ADVISED HIM THAT THE HELI WAS NO FACTOR. AT THE TIME THAT HE WAS ADVISING ME THAT HE WAS GOING AROUND; THE ACFT NOSED UP SO I GAVE HIM INSTRUCTIONS TO GAR AND HE LANDED AFTER THAT. THE TWR SUPVR TALKED TO THE COPLT AFTER THAT AND WE FOUND OUT THAT THE TCASII EQUIP ON THE PLANE WAS GIVING THEM A 'CLB UP' WARNING. LUCKILY; TFC WORKLOAD WAS LOW. I THINK THE ACCURACY OF THE TCASII EQUIP SHOULD BE REVIEWED AND PLTS SHOULD NOT RELY MAINLY ON IT. IF POSSIBLE; CONFIRM WITH ATC BEFORE EXECUTING EVASIVE MANEUVERS.