HS25 ON VISUAL APCH TO BKL HAS A VERY CLOSE CALL WITH A SMALL CESSNA IN THE TFC PATTERN.

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WE WERE CLRED FOR THE VISUAL APCH TO RWY 24R AT BKL. UPON CONTACTING THE LCL CTLR AND RPTING INBOUND; SHE DEMANDED OUR IDENT; AND STATED THAT WE WERE NOT AUTH TO BE IN HER AIRSPACE. I AGAIN RPTED OUR CLRNC AND POS TO HER AND SHE REPLIED WE WERE SUPPOSED TO BE W OF THE ARPT. I STATED THAT WAS IMPOSSIBLE AS WE WERE VECTORED E OF THE ARPT AND ONTO FINAL BY THE APCH CTLR. AS SHE CONTINUED TO QUESTION WHO WE WERE; I NOTICED A TARGET ON THE TCASII RAPIDLY DIMINISHING IN DISTANCE DIRECTLY IN FRONT OF US ALIGNED WITH THE SAME RWY. AS WE WERE STILL DSNDING TO THE RWY. I FINALLY WAS ABLE TO MAKE OUT A SINGLE ENG ACFT IN THE BASE NO MORE THAN 1 MI IN FRONT OF US. THE CTLR HAD ZERO SITUATIONAL AWARENESS AND OFFERED NO RESOLUTIONS TO THE PROB. WE STATED AND INITIATED AN IMMEDIATE GAR AND CIRCLED BACK AND LANDED WITHOUT INCIDENT. THE CTLR OFFERED NUMEROUS APOLOGIES TO US AND STATED THAT SHE WAS MISINFORMED OF OUR POS INBOUND. THE CTLR APPEARED VERY CONFUSED AND EXCITED AND DURING THIS EPISODE; FREQUENTLY MISIDENTED OTHER ACFT IN THE AREA. THIS APPEARS A SERIOUS MISCOM PROB WITH THE LCL AND APCH CTL FACILITY; AND A TOTAL LACK OF SITUATIONAL AWARENESS ON THE PART OF THE LCL CTLR.