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When the driver threatened to call police she allegedly punched him in the face, before the shocked driver appeared to slap her back.
Police said the girl again began punching the driver in the face as he tried to film the damage to his car, then allegedly stole it and drove away on Albert Street.
She then allegedly crashed the car into a parked vehicle nearby and fled.
The girl, who police said was of Aboriginal appearance, was wearing tight, dark clothing including a singlet with the Oakland Raiders NFL team logo on it.
Her hair was tied into two narrow braids that hung over her shoulders - and were sent flying when the taxi driver appeared to slap her.
Police were hunting the girl over the incident but have not made any arrests.