The old Hall of Records was indeed a nice building. Too bad it had to be demolished.
Here it is in its last days, with the Criminal Courts Bldg. being constructed right up against it in 1970:
1973:
Being demolished later in 1973:
Of course the building is at an odd angle on the block because it followed the old street pattern before they were widened and realigned:
1924
All pics from lapl.org