A BE400 FLT CREW BEGAN TO CLB BEFORE REACHING THE 4.5 DME REQUIREMENT WHILE ON THE TEB 5 DEP.

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AFTER A LONG WAIT FOR ENGINE START; TAXI AND TKOF (GND STOP FOR WX); WE WERE ISSUED A TKOF CLRNC. WE WERE ASSIGNED THE TEB 5 DEP OFF OF RWY 24. UPON TKOF AND CLBOUT; WE FOLLOWED THE PROC. UPON REACHING 1500 FT MSL; I ASKED MY CAPT IF I SHOULD WAIT UNTIL PASSING 4.5 DME AND THEN CONTINUE THE CLB TO 2000 FT MSL. HE TOLD ME TO CONTINUE TO 2000 FT MSL. I ASKED HIM TO VERIFY THAT THERE WAS NO DME REQUIREMENT BEFORE CONTINUING UP TO 2000 FT MSL. AGAIN; I WAS TOLD TO CONTINUE MY CLB BY MY CAPT. AT APPROX 3.7 DME FROM TEB VOR; I VACATED 1500 FT FOR 2000 FT MSL. UPON PASSING THROUGH 1800 FT MSL; MY CAPT FOUND THE 4.5 DME BEFORE LEAVING 1500 FT MSL REQUIREMENT AND TOLD ME TO GET BACK TO 1500 FT MSL. AT ABOUT THE SAME TIME; NY DEP CAME ON THE RADIO AND STATED; 'YOU DIDN'T COMPLY WITH THE SID AS INSTRUCTED.' WE RETURNED TO 1500 FT MSL UNEVENTFULLY AND WITHOUT TFC CONFLICTS OR ALERTS. FACTORS CONTRIBUTING TO THIS WERE: MYSELF VACATING 1500 FT MSL PREMATURELY BEFORE HAVING MY CAPT VERIFY IT. WHILE I DID QUESTION THE DME REQUIREMENT; I SHOULD HAVE NOT LEFT THE ALT UNTIL MY CAPT HAD VERIFIED IT DESPITE HIM TELLING ME TO DO SO AND TELLING ME TO CLB TO 2000 FT MSL AND THAT THERE WAS NO DME REQUIREMENT. WHILE WE DID LEAVE 1500 FT MSL EARLY; WE PROMPTLY RETURNED WHEN WE DISCOVERED WE ERRED.