TR6SC
I live for the CABE
Not too sure about free in LA, Amigo, but I believe you're right about the stolen part.I don't believe there was a tax or charge for registering a bicycle with the town or city, I think it was strictly to identify a bike if it was stolen. I may be wrong, some cities and townships might have charged to register your bike and get a tag, but I believe they were free, all you had to do was bring your bike to the police department and they would record the serial number and issue you a license plate.
I remember going up to the Hollywood precinct on Wilcox and De Longpre and giving the officer a dollar. It was all very official, like the DMV. At the mid-turn of the Century (the 50s), the licenses were water slide decals. I remember that dollar. It was a lot of money.