A Dash 8 flight crew reported experiencing an apparent phantom target TCAS event on approach into LGA near HPN.

Narrative

On approach into LGA approximately 18 miles north of the airport on the ILS 22 Localizer; we encountered a TCAS RA. We were level at 4;000 FT; and just issued a new clearance to descend to 3;000 FT. Immediately after receiving the new clearance; a TCAS RA was annunciated and a traffic conflict displayed. Our instructions were to climb; climb now; with a climb rate in excess of 1;500 FPM. While I initiated the RA response; [the] Captain; who was the pilot not flying; began to search for traffic and told ATC of our actions. The traffic was displayed for no more than 5 seconds and then disappeared. I did not climb to more than 4500 FT. Since we were unable to find the traffic; in VFR conditions; and the short duration of the RA we assumed it was a phantom target. We informed ATC of our suspicion that the RA was due to a phantom target and we were returning to our assigned altitude of 4;000 FT; and confirmed the continued descent to 3;000 FT instruction. The only other information that I would like to add is that this RA happened in close proximity to HPN which is why we took it as a severe threat at first; however after not seeing any traffic; realized it was probably some sort of phantom target.