IFR ACR DEP FROM SJC; AFTER TWR CLOSED; FAILED TO OBTAIN DEP RELEASE PRIOR TO TKOF.

Narrative

UPON LNDG IN SJC; THE TWR ADVISED THAT THEY WOULD BE CLOSING WITHIN SECONDS AND WOULD WE LIKE OUR OUTBOUND CLRNC. AFTER CLRING THE RWYS AND COMPLETING THE AFTER LNDG DUTIES; WE TOOK THE CLRNC. IN THE SAME SENTENCE (NEARLY); THE CTLR ANNOUNCED THAT 'THE SJC TWR WAS NOW CLOSED.' HE DID TELL US THAT WE WOULD NEED TO TALK TO DEP CTL WHEN WE TOOK OFF AND THAT THERE WERE FURTHER INSTRUCTIONS ON THE ATIS (THERE WERE NOT). THE IMPRESSION I HAD WAS THAT WE WERE TO DEPART AND CALL NORCAL AIRBORNE. IT WAS A VERY NICE NIGHT; WX WISE. OTHER COMPANY AIRPLANES WERE DEPARTING AND WE COULD SEE EVERYONE. WE DEPARTED SHORTLY AFTER COMPANY AND CALLED NORCAL DEP. HE SEEMED SURPRISED TO HEAR FROM US AND ASKED IF WE HAD A CLRNC; WHICH WE DID. IT TOOK A MOMENT BEFORE WE REALIZED HE WAS TALKING ABOUT A DEP RELEASE. HE TOLD US TO GET ONE IN THE FUTURE AND CONTINUED OUR CLB AND DEP. IT HAS BEEN YRS SINCE I HAVE DEPARTED FROM AN ARPT WITH A CLOSED TWR. I DIDN'T TAKE THE TIME TO PULL OUT THE BOOK AND VERIFY THE PROC. WHENEVER SOMETHING UNUSUAL OCCURS; I NEED TO PULL OUT THE BOOK AND VERIFY. THE TWR CTLR'S INSTRUCTIONS COULD HAVE BEEN A LITTLE MORE HELPFUL. IF HE WOULD HAVE SAID; 'CALL DEP CTL FOR A DEP RELEASE; GOOD NIGHT;' THAT WOULD HAVE HELPED TO GIVE US A BETTER CLUE.