AFTER XFER OF COM FROM PCT TO ZDC; B717 FLC INITIATED TCASII EVASIVE MANEUVER DUE TO A CONFLICTING CARJ.

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AFTER TKOF FROM BWI; APCH CLRED US TO 8000 FT AND GAVE US A HDG OF 220 DEGS. WE THEN CONTACTED WASHINGTON APCH. WASHINGTON APCH GAVE US 17000 FT; AND STILL THE SAME HDG. WHILE THEY WERE HANDING US OVER TO ZDC; THEY GAVE US A CLRNC TO EXPEDITE THROUGH 20000 TO 23000 FT. AT THE MOMENT; HE SAID THAT WE GOT A RED BOXED CORRECTIVE (RA) TO DSND 1500 FPM -- WE WERE CLBING AT THE TIME 2800 FPM. THE CAPT TOOK THE AIRPLANE OFF AUTOPLT; INITIATED A DSCNT; AT THAT TIME IT SAID 2500 FT DOWN ON THE TCASII. THE ACFT WAS TO OUR R. I VISUALLY SAW HIM AT 2 O'CLOCK POS. I LOOKED BACK AT THE TCASII; AND IT SAID WE NEEDED 4000 FT DOWN; WHICH HE (CAPT) DID. THE CTLR SAID DON'T WORRY; TO CLB ANYWAY. I RESPONDED THAT WE HAD AN ALERT AND WERE DSNDING. HE SAID TO KEEP CLBING. I RESPONDED; WE ARE DSNDING; HE SAID; YOU'LL BE OK. THEN HE SAID TO DO WHAT WE NEEDED TO DO. THOSE WERE HIS EXACT WORDS. I LOOKED TO THE R AND SAW THE ACFT EVER SO CLOSE OFF THE R SIDE -- PASSING OVERHEAD; OVER OUR TAIL AT ABOUT +100 FT; TCASII SHOWED '+ 100 FT' RA RED BOX. AT THE TIME HE PASSED OVERHEAD; WE WERE AT A MAX 6000 FPM DSCNT! WE ARE STILL UNSURE WHY HE SAID IT WOULD BE OK TO CLB.