I don't know if the italian Veneti were related to the gaulic Veneti. Some people think they were, but it is probably just a coincidence with both tribes having the same name, leading to wild speculations.
It is sometimes difficult to tell if a tribe was celtic or just celticised in language and culture. It depends how you define "celtic", tribes with the same language and culture aren't always genetically related and related tribes don't need to have the same culture and language. It is even debated if ancient Britain was populated by Celts (meaning Hallstatt and La Tene culture) or by people heavily influenced by Celts and thus speaking celtic languages.
Wikipedia (which is not an academic source of course!) lists three ancient peoples called "Veneti", stating that they are not related to each other.
http://en.wikipedia.org/wiki/Veneti
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