A GULFSTREAM 4 CREW; FLYING UNDER PART 135; WERE INSTRUCTED TO DSND TO 3000 FT; BUT THEY STOPPED AT 4000 FT. THE N90 CTLR ADVISED THE CREW OF TFC AND REQUESTED AN IMMEDIATE DSCNT TO 3000 FT.

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ON ARR INTO TETERBORO; WE WERE CLRED DOWN TO 4000 FT. AFTER BEING AT 4000 FT FOR SOME TIME; CTLR ASKED US WHY WE STOPPED AT 4000 FT AND SAID WE SHOULD BE AT 3000 FT. WE DO NOT REMEMBER BEING CLRED TO 3000 FT. OPPOSITE DIRECTION TFC APPEARED ON TCASII 200 FT BELOW US. WE DSNDED TO 3000 FT WITH NO TFC CONFLICT. SUPPLEMENTAL INFO FROM ACN 468852: THE LEG IN QUESTION WAS BEING CONDUCTED UNDER FAR 135 CHARTER OPS. ATC HAD CLRED US TO DSND TO 4000 FT AFTER PASSING THE MUGZY INTXN. SHORTLY AFTER THAT; WE WERE GIVEN RADAR VECTORS FOR WHAT WE THOUGHT WAS GOING TO BE THE VOR DME A APCH; CIRCLE TO LAND RWY 19 AT TEB. I ADVISED CAPT THAT I WOULD BE OFF THE ATC FREQ JUST LONG ENOUGH TO CONFIRM THE LATEST ATIS. WITHIN A COUPLE OF MINS OF MY RETURN TO THE ATC FREQ; WE RECEIVED AN URGENT COMMAND FROM ATC TO DSND IMMEDIATELY TO 3000 FT. CAPT REACHED FOR THE VERT SPD SELECTOR ON THE FLT GUIDANCE CTLR TO SELECT A DSCNT WITH THE AUTOTHROTTLES WHILE THE ACFT WAS STILL ON AUTOPLT. I IMMEDIATELY ADVISED THE CAPT TO 'GET RID OF THE AUTOMATION; AND GET US DOWN AS SOON AS POSSIBLE.' WE HAD THE TFC IN QUESTION CLRLY IN SIGHT AND ON THE TCASII ABOUT 5 OR 6 MI AWAY. WHEN I QUESTIONED CAPT; 'DID YOU RECEIVE THE ATC CLRNC TO 3000 FT WHILE I WAS OFF THE ATC FREQ?' HIS RESPONSE WAS SOMETHING TO THE EFFECT OF 'I CANNOT REMEMBER IF IT WAS 4000 OR 3000 FT.' CAPT'S DELAY (ATTEMPTING TO USE THE AUTOMATION FOR THE DSCNT) MAY HAVE CAUSED US TO LOSE IFR SEPARATION.