Bicycles have serial numbers
, but usually don't have VIN
's at all.
There is a chance of some confusion here--because with a vintage or antique example of a motorized bicycle, it may be possible to register it without a VIN, or it may be possible to request a VIN for it (IL is one state that will grant VINs to antique/vintage vehicles). States write their laws so that if a particular vehicle was ever allowed to be registered in the past, then they will always have provisions for it to be re-registered--but they won't necessarily allow you to construct a new example and register that.
When you e-mail your dept of motor vehicles about motorized bicycle laws, you need to be very specific: you should ask them about taking a new bicycle and adding an engine yourself
. You should not ask simply about "motorized bicycles", because there are probably provisions for allowing registration of vintage and antique
examples of motorized bicycles (previously registered!) that your new-built motorized bicycle will not qualify under.