ACR MLG DISPUTES DELAYS DSCNT UNTIL TCASII TFC PASSES BELOW THE ACFT. N90 CLAIMS THERE WAS NO TFC AND THAT TCASII SHOULD BE REMOVED FROM ALL ACFT AND CTL RETURNED WHERE IT BELONGS -- WITH ATC.

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AT 3500 FT; PROCEEDING UP THE HUDSON RIVER (AS DIRECTED); WHEN APCH CTL (LAGUARDIA APCH CTL 125.85) DIRECTED US TO DSND TO 3000 FT AND TURN R TO 040 DEG. AT THIS SAME TIME; WE RECEIVED A TA ON THE TCASII RADAR; INDICATING TFC AT APPROX 3 MI AHEAD (12 O'CLOCK) AND 900 FT BELOW. IMMEDIATELY THEREAFTER; WE RECEIVED AN RA DIRECTING US TO 'MONITOR VERT SPD'; ACCOMPANIED BY VVI INDICATOR RED LIGHTS ILLUMINATED AT ALL POINTS BELOW 0. WE ADVISED APCH CTL THAT WE WERE UNABLE TO DSND UNTIL TFC CONFLICT PASSED DUE TO TCASII RA. HE (THE APCH CTLR) SAID THERE WAS NO TFC AND THAT TCASII EQUIP SHOULD BE REMOVED FROM ALL ACFT AND CTL BE PLACED BACK WHERE IT BELONGS -- WITH ATC. ALSO; HE INDICATED THAT WE SHOULD FILL OUT A RPT; THAT HE WOULD DO THE SAME. AT THIS POINT; THE TCASII CONFLICT PASSED WHICH WAS ELECTRONICALLY VERBALIZED BY THE TCASII. THE TFC IN QUESTION APPEARED NOT TO BE A 'GHOST'; REMAINED AT APPROX 2600 FT MSL AND PASSED FROM IN FRONT OF US TO BEHIND US. WE DID NOT; HOWEVER; ACTUALLY SEE THE TFC. RECOMMEND ATC CTLRS BE BETTER VERSED ON THEIR RESPONSIBILITY CONCERNING TCASII RA'S. THE RADIO TRANSMISSIONS FROM THE CTLR IN THIS CASE ONLY ADDED TO THE ANXIETY IN THE COCKPIT AND PRESENTED HIM AS BEING LESS THAN PROFESSIONAL.