A B737-300 FLC RECEIVED A TCASII TA ON CLB FROM SEA.

Narrative

WE WERE DEPARTING SEA ON THE SUMMA 5 DEP SID; USING RWY 34R. AT THE 8 MI FIX; WE TURNED R TO A HDG OF 070 DEGS AS PER THE SID. WE PREVIOUSLY HAD BEEN CLRED TO 15000 FT WHEN WE HAD CONTACTED DEP CTL SHORTLY AFTER TKOF. (INITIAL ALT CLRNC ON THE GND FROM PDC HAD BEEN 9000 FT.) WE WERE NOW ON A HDG OF 070 DEGS WHEN ATC (DEP) CALLED 'TFC AT 10 O'CLOCK; 10000 FT; HIGHER WHEN CLR.' NEITHER PLT HEARD A DIRECTIVE TO 'MAINTAIN 9000 FT.' I 'ROGERED' THE TA AND LOOKED FOR THE TFC. (THE ADVISORY OCCURRED AS OUR ACFT WAS CLBING THROUGH 7000-8000 FT.) APCHING 9000 FT; I VISUALLY ACQUIRED THE OTHER ACFT AT 10000 FT; 10 O'CLOCK. AT ABOUT THE SAME TIME; OUR TCASII ANNOUNCED THE 'TFC.' (WE DID NOT RECEIVED AN RA.) I ADVISED THE COPLT; WHO WAS FLYING; AND HE BEGAN TO LEVEL OUR ACFT. SHORTLY THEREAFTER; WE RECEIVED A CALL FROM ATC TO 'DSND TO 9000 FT.' WE ACKNOWLEDGED 'DSNDING TO 9000 FT;' AND THE HIGHEST WE REACHED WAS APPROX 9300 FT. I BELIEVE A CONTRIBUTING FACTOR TO THIS INCIDENT WAS THE LACK OF A CLRNC TO 'MAINTAIN 9000 FT' AFTER THE TA. (I CALLED SEA TRACON LATER AND CONFIRMED THAT NO 'MAINTAIN 9000 FT' HAD BEEN ISSUED.)