When I was in my youth I painted model airplanes with a nitrocellulose paint called dope. The term was/is also common among drug users, and has long been a synonym for "stupid" or "incompetent."
While dope the paint still exists http://www.randolphaircraft.com/210dope.html that meaning is no longer in common use. Is there any connection between the three meanings? Since the inhalation of the paint will intoxicate a person, could the other two terms have derived from that unfortunate quality, or do they exist sans connection?

According to the entry on dope in the OED2, they are all of the same origin: Dutch doop 'sauce'. The paint, drug, and stupid person meanings have citations from the 19th century.