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The cat's owner was in tears following the late-morning attack.
The attack took place at the lower end of Dundonald St, in Tainui.
The young woman accompanying the dog at the time of the attack was distraught and was being comforted by her mother, amid a heavy police presence.
Dunedin City Council compliance, animal and parking services team leader Peter Hanlin said an investigation was under way.
''A range of actions are possible, including a menacing classification, a fine or prosecution under the Dog Control Act.
''Animal Services officers will consider factors including the circumstances of the incident and the history of the owner and the dog.''
He described the dog as a ''terrier breed'' but would not be more specific.
A neighbour who witnessed the attack, who did not want to be identified, described the dog as a ''pit bull''.
The mother and daughter who apparently owned the dog drove away with their pet.
-Dunedin police (03) 471-4800, Crimestoppers 0800-555-111.