BAE125 CREW RECEIVED TCASII RA CLBING TO FL250.

Narrative

DURING INITIAL CLB OUT OF YIP; WE WERE CLRED TO FL240. I RECEIVED A CLRNC TO FL250; SET FL250 IN THE ALT SELECT; AND READ BACK THAT I WAS GOING TO MAINTAIN FL250. (AT THIS TIME THE AUTOPLT WAS ENGAGED AND I WAS WORKING THE RADIOS DUE TO THE FACT THAT THE FO WAS INVOLVED IN PUTTING AWAY CHARTS AND VERIFYING RTES AND FREQS.) I RECEIVED A FREQ CHANGE FROM ATC. I CHKED IN WITH ZOB AND STATED THAT I WAS PASSING FL180 FOR FL250. I WAS TOLD I WAS STILL WITH THE LOWER GUY. I APOLOGIZED AND SAID I MUST HAVE FORGOT TO PUSH THE BUTTON. I THEN PRESSED THE FLIP-FLOP SWITCH AND STATED TO ZOB THAT I WAS PASSING FL190 FOR FL250. CTR ACKNOWLEDGED AND STATED NOTHING FURTHER. SHORTLY AFTER THE CHK ON; THE FO WAS BACK TO MAKING THE RADIO CALLS. WE RECEIVED A TA FROM TCASII AND STARTED SEARCHING FOR A VISUAL ON THE TFC. AS THE FO SPOTTED THE TFC WE RECEIVED AN RA FROM TCASII TELLING US TO 'DECREASE CLB.' I STOPPED THE CLB AT FL242; JUST AS I HEARD THE CTLR SAY THAT IT LOOKED LIKE SOMEONE DIDN'T LEVEL OFF. I ASKED THE FO TO CONFIRM OUR ALT CLRED TO; AND ATC SAID IT WAS FL240 AND ASKED WHAT WE WERE LAST CLRED TO. THE FO RELAYED THAT I SAID IT WAS FL250 AND THAT I HAD STATED SO WHEN CHKING IN. ATC SAID NO; IT WAS FL240. BY THIS TIME I WAS BACK DOWN TO FL240 AND LEVELED OFF. TO THE BEST OF MY KNOWLEDGE; THE OTHER TFC HAD NOT RECEIVED ANY WARNING AND WAS UNAWARE OF THE SIT UNTIL WE ASKED CTR TO VERIFY OUR ALT CLRNC.