A DEHAVILLAND DASH 8 HAD AN NMAC NEAR HAR.

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ZNY CALLED TFC AT 10 O'CLOCK; 5 MI. I WAS PNF. I INDICATED NEGATIVE CONTACT; ONE AT 11 O'CLOCK -- HE POINTED HIM OUT. PF POINTED TO HIM; SO I 'FIGURED' HE HAD THE TFC. I INDICATED TO ARTCC WE HAD VISUAL CONTACT (WE SAW HIS LNDG LIGHTS BLAZING). ARTCC SAID MAINTAIN VISUAL SEPARATION AND I THINK SOMETHING TO THE EFFECT OF DSNDING HIM THROUGH OUR ALT; WE WERE CLRED TO CLB. CLOSING QUICKLY; WE GOT A TCASII TA BUT I STILL BELIEVED THE PF HAD TFC. HE WAS HAND FLYING; NOT USING AUTOPLT; SO ATTN WAS INSIDE MORE THAN OUTSIDE. I DIDN'T GET A DEFINITIVE RESPONSE. THEN TCASII RA 'DSND; DSND' ACFT WAS 1/2 MI; 200 FT ABOVE. THE CAPT KEPT CLBING; LOOKING OUT WINDOW; THEN TURNING R. I KEPT ASKING 'YOU GOT HIM?' HE WAS OFF L SIDE; SO I COULD NOT SEE. ALL I SAW WAS TCASII SHOWING +02; +01; 00! AND TARGET WAS RIGHT ON OUR MINIATURE AIRPLANE SYMBOL. BY THIS TIME; HE HAD PULLED THE PWR LEVERS TO FLT IDLE! THAT'S IT. I DIDN'T KNOW IF HE HAD THE TFC OR NOT; SO I PUSHED THE YOKE UNTIL WE GOT A GOOD DSCNT GOING AND I SAW +01; +02; +03; THEN LET OFF THE YOKE PRESSURE. LATER HE TOLD ME HE DIDN'T EVEN FEEL ME DO THAT. ACCIDENT WAS AVOIDED -- TOO CLOSE; THOUGH. HE SAID HE WAS ANGRY SINCE HE 'NEVER' CALLS TFC TO ATC. THAT'S THEIR JOB. TO SOME DEG; I AGREE; BUT WE SAW THE OTHER ACFT. BUT MY MISTAKE WAS CALLING TFC AND ACCEPTING VISUAL SEPARATION WITHOUT CAPT'S CONCURRENCE. I WILL ASK FUTURE PLTS THAT I FLY WITH HOW THEY WISH TO HANDLE ATC TA'S. AS A NOTE: PF (CAPT) SAID 'I'M BAD LUCK THINGS HAPPEN TO ME (WHAT THE %$#@ IS THAT?) HE TOOK NO PROACTIVE ACTION. I HAD TO PUSH THE YOKE MY HUMAN FACTOR I MENTIONED HIS IS APPARENT.