C182 HAS NMAC WITH A TWIN PIPER ON DOWNWIND LEG OF RWY 27 AT CDW; A TWR CTLED ARPT.

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I WAS FLYING A TCASII EQUIPPED C182G. I WAS IN THE R TFC PATTERN FOR RWY 27 AT CDW. I WAS DOING STOP-AND-GOES AT NIGHT. I WAS UNDER CTL OF THE TWR IN THE CLASS D AIRSPACE. I HAD TURNED XWIND AFTER A CLB FROM THE SECOND OF 3 STOP-AND-GOES; THIS FINAL ONE CULMINATING IN A FULL STOP AND TAXI BACK TO OUR HANGAR. A PIPER (LOW WING) WAS ENTERING THE PATTERN; STRAIGHT INTO THE DOWNWIND LEG; AND WAS ABOUT 500 FT ABOVE ME. I HAD THE PIPER IN SIGHT DURING MY XWIND CLB. THE PIPER APPARENTLY CAME OVER TO THE TWR FROM NEW YORK TFC CTL. THE PIPER HAD PROBS FOLLOWING INSTRUCTIONS WITH NEW YORK TFC CTL. CDW TWR POINTED US OUT TO THE PIPER AS TFC. THE PIPER CLAIMED TO HAVE US IN SIGHT. TWR INSTRUCTED THE PIPER TO FOLLOW ME AND WAS #2 TO LAND. I THEN TURNED DOWNWIND LEG. THE CDW TWR CTLR THEN BEGAN TO XMIT A PROLONGED CONVERSATION TO THE PIPER ABOUT COMPLETING INSTRUCTIONS GIVEN BY CTLRS. WHILE I WAS IN THE DOWNWIND LEG AT TFC PATTERN ALT; THE PIPER BEGAN TO DSND INTO THE TFC PATTERN ON TOP OF ME. MY TCASII BEGAN TO ANNOUNCE 'TFC' AND I WATCHED THE PIPER DSND ON TOP OF ME. THE PIPER ON TCASII BEGAN AS 500 FT ABOVE ME. IT GRADUALLY DSNDED UNTIL TCASII RPTED ZERO DIFFERENCE IN ALT AND MERGED WITH ME AS ONE TARGET. I WAS NOT ABLE TO XMIT THE IMPENDING MIDAIR COLLISION BECAUSE THE CTLR WAS XMITTING HIS LECTURE OVER THE FREQ. I IMMEDIATELY ASKED MY R SEAT PAX (A PVT PLT) WHERE THE TFC WAS. HE RPTED THE TFC WAS BEHIND US ON HIS SIDE AND AT THE SAME ALT AND 150 FT AWAY. I MANEUVERED TURNING L AND DIVING TO AVOID THE COLLISION. WHEN THE CTLR FINALLY GOT OFF THE FREQ; I RPTED THAT TCASII HAD REVEALED TFC AS TOO CLOSE AND REQUESTED THAT I BE ALLOWED AN EXTENDED DOWNWIND LEG SO THAT THE PIPER COULD LAND. THE CTLR TOLD ME I WAS #1 TO LAND AND THAT I WAS CLRED TO LAND. HE STATED THAT THE PIPER WOULD BE #2 TO LAND. I THEN LANDED. THE PIPER FOLLOWED ME DIRECTLY AROUND BASE AND FINAL; DISREGARDING TWR'S INSTRUCTIONS TO EXTEND HIS DOWNWIND; AND LEAVING SO LITTLE SEPARATION THAT THE TWR NEEDED TO EVENTUALLY CALL OFF THE PIPER'S LNDG AND FORCE THE PIPER TO DO A GAR. MY PAX (COPLT) THEN REQUESTED THE TELEPHONE NUMBER TO THE TWR TO DISCUSS WHAT HAD HAPPENED. HE THEN HAD A CONVERSATION WITH THE CTLR WHO CLAIMED WE WERE AT LEAST 200 FT APART. THE PLANES WERE ALLOWED TO GET TOO CLOSE. I KNOW THAT THE PLTS ARE RESPONSIBLE FOR SEPARATION IN CLASS D AIRSPACE. HOWEVER; THE TWR CTLR'S EXTENDED CONVERSATION DID NOT ALLOW ME TO XMIT MY CONCERN. HIS INSTRUCTIONS TO A LOW WING PIPER TO DSND INTO THE TFC PATTERN ON TOP OF A HIGH WING CESSNA CONTRIBUTED TO THIS SIT. HIS LECTURE ALSO PROBABLY CAUSED THE PIPER PLT TO LOSE CONCENTRATION AND LOSE HIS TFC (ME). THE CTLR SHOULD HAVE HAD THIS CONVERSATION WITH THE PLT ON THE GND.