sign out of some place
sign someone out of some placeand sign someone out
to make a record of someone's departure from some place. Did someone sign you out of the factory, or did you just open the door and leave? I signed out those two who just left.
sign something out of some placeand sign something out
to make a record of the borrowing of something from some place. Dave signed the tape recorder out of the library. Dave signed out the tape recorder as well as some blank tapes.