A car sped along Napier Street - at times on the wrong side of the road - and narrowly avoided several collisions, police said.
The dark blue, early-model BMW was driven away from police at the intersection of Napier and Lyons streets about 2.20pm on Thursday.
Police said several other drivers had to brake or swerve to avoid crashing into the vehicle as it ran through a red light.
The car was followed along Napier Street until the intersection at Scott Street, where the driver again drove through a red light, narrowly avoiding crashing into turning traffic.
Officers lost sight of the vehicle, but a witness called triple zero a short time later to report a blue BMW driving on the wrong side of the Midland Highway at Epsom.
Anyone with dash cam footage of the vehicle, or who saw the car's registration plate, is urged to contact Senior Constable Ian Kuster at the Castlemaine police station on 5470 4100.
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