A CJ3 had a near miss with a VFR C172 approaching TEB in IMC.

Narrative

We were on vectors approaching TEB. While heading 120 at 3;000 FT; traffic was called at 12 o'clock less than a mile. We advised that we were in the clouds. Then given a heading of 090 and advised of a traffic alert. During the turn we broke out of the clouds and saw the traffic at 12 o'clock and about 100 FT below us. We made a right turn and passed behind the Cessna 172 probably less than 300 FT horizontally and advised ATC. We were then given a heading of 110. The other aircraft was operating VFR and not talking to ATC; although I found out later that he had tried to call them and couldn't make contact. He was climbing through our altitude at the time and if he had legal cloud clearance; it was minimally so. I obtained both the ATC voice tapes and two different radar plots of the tracks of both aircraft. They confirm that we passed with less than 100 FT vertical and less than 300 FT horizontal. The CJ3 is not equipped with TCAS II so we only got a traffic alert; not an RA. ATC did not identify the aircraft to us until we were very close. We were in the clouds at the time. The other aircraft was operating VFR in marginal IFR legal conditions. The initial avoidance heading given by ATC turned us directly at the other aircraft (not really sure if it was an avoidance vector; or if it was just a heading; then the traffic alert). I contacted the other pilot involved and discussed it with him. He was not aware the near miss had occurred.