I have always called my local police station, politely say you are looking at buying a parts bike, but want to be sure its clean/clear. They usually transfer me to a dispatcher and they run the vin for me. If they are in a good mood get them to run it in the state you are in and purchasing from(if different).
Have only been turned down 1 out of the 7-8 parts bikes i've purchased. The one time the dispatcher was having a bad day. I just called back the next day and got a different person who was glad to help.
Have never called for mopeds though, you might mention that you are looking to run the VIN for a 19XX moped. They might have a different way of searching for that type of property.