A shot has allegedly been fired at police as officers attempted to arrest the driver of a stolen Lexus in Sydney’s inner west.

Officers initially spotted the car in Petersham about 3:15am and initiated a pursuit, police said, before losing sight of the car.

Police said the vehicle was then spotted a short time later on New Canterbury Road before the male driver was seen running from the car into an alleyway.

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It was then that the driver of the car allegedly turned to police and fired a single shot at the officers in pursuit, hitting a building.

He was arrested and taken to Newtown Police Station.

A 20-year-old woman, believed to have been a passenger, was arrested and taken to hospital with an arm injury.