The violin was invented in Italy.

The fiddle bow is thought to have been invented in the spice islands of Indonesia. Its transmission to Europe via the Roma is not impossible, but I would look to Near Eastern and Mediterranean merchants for the transmission vector before I looked to the Roma. Furthermore the Roma didn't reach Western Europe until circa 1400 (though they were in eastern Europe earlier). The bowed fiddle was known in the west before then. Even if the Roma introduced the fiddle bow to eastern Europe, it preceeded them to western Europe. Besides that, it's not known when the Roma left India. It may have been that the Roma were out of touch with the Islands of east Asia (if they ever had contact at all) before the fiddle bow was invented there.

T.