PIC RPT ON NEEDLESS TCASII RA ON EVASIVE ACTION CLB DURING DEP PROC. ARR TFC ON MAP AND TURNING TO DOWNWIND. DEP TFC STRAIGHT OUT.

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RIGHT AFTER TKOF FROM KMMU AND CLBING TO 2000 FT WE GOT A RA EVENT ON OUR TCASII AT 1500 FT. IT COMMANDED A HIGH RATE OF CLB INCREASE WHICH WE DID THROUGH 2000 FT. WE WENT TO 3000 FT BEFORE WE COULD LEVEL OFF TO GO BACK DOWN TO 2000. WE IMMEDIATELY ADVISED NEWARK DEP CTL THAT WE WERE DOING AN RA AND WHAT ALT WE WERE AT AND DSNDING BACK TO 2000 FT. DEP CTL DIDN'T LIKE WHAT WE HAD DONE. NO ONE HAD TO TAKE EVASIVE ACTION BECAUSE OF US. MORRISTOWN TWR DIDN'T ASK IF WE HAD ANY TFC IN SIGHT; HE JUST ADVISED US THAT A GUY WAS ON APCH AND HAD BROKEN IT OFF AND HAD ENTERED DOWNWIND TO THE RWY WE WERE TAKING OFF FROM. I'M GUESSING THAT MIGHT HAVE CAUSED THE RA. WE NEVER SAW THE ACFT VISUALLY; JUST ON TCASII; ABOUT 1/2 MI FROM US. WE WERE CLBING AT ABOUT 2000 FPM; 180 KTS INDICATED WHEN WE GOT THE RA. IT INCREASED OUR RATE OF CLB TO 5000 FPM UNTIL WE WERE OUT OF THE RA EVENT. THAT'S WHY WE WENT TO 3000 FT BEFORE WE COULD START BACK DOWN TO 2000 FT. I WOULD RECOMMEND THAT TWR MAKES SURE THE PLT HAS TFC IN SIGHT (WHEN OPERATING WITH TCASII) BEFORE CLRING FOR TKOF.