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The truck rolled in Jervois St near the intersection with Cumberland St about 10am today, a police spokeswoman said.
No-one was injured, but "four to five" parked cars were damaged as a result, she said.
A Fire and Emergency New Zealand spokesman said firefighters from Dunedin City and Willowbank attended to help with cordons and to clean up diesel which leaked from the truck.
Police inquiries are continuing.