You can take your dog on the Vaporetto but don't forget to bring a leash and muzzle. Always carry a pooper-scooper and plastic bag to keep your dog from soiling the city. The fine can be quite high, from €25 up to €500.
www.comune.venezia.it/flex/cm/pages/ServeBLOB.php/L/EN/IDPagina/144#abe1c6
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