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They are urging members of the public who report suspicious activity to note down car registrations if possible.
Acting Inspector Craig Dinnissen, of Dunedin, said a serious assault in a car was reported in Elgin Rd, Mornington, on Monday afternoon.
''A male Maori passenger in a vehicle was seen hitting the female in the driver's seat of the car.''
The red maroon hatchback was stationary but the witness did not record its registration, and the offender was yet to be located, Insp Dinnissen said.
Across town in St Kilda that same day, another witness saw an older model grey Nissan Skyline being driven erratically along Richardson St.
The driver then stopped the vehicle, lifted a possibly unconscious or intoxicated woman off the ground and bundled her into his vehicle before driving off down Ajax St.
''It's another one where it's been reported but we haven't got a registration,'' Insp Dinnissen said.
''Ideally, if people are going to report things, we really need at least the registration.''