The chase started after police found an unregistered Mercedes Benz on William Street about 3.30am Saturday.
Police allege the car fled before running a red light and stopping in Little Bourke Street, where the five people inside took off on foot.
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A man was arrested nearby who was identified as an off-duty police officer from the north-west metro region.
The 28-year-old officer is expected to be charged on summons with drug possession and has been suspended with pay.
A second off-duty police officer was also identified in the pursuit.
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