Officers say they were called to an alleged smash involving a car and two parked motors on Thornwood Avenue in the West End on Wednesday, August 14.
The force was alerted to the incident at around 11.50pm.
However, according to police, the two occupants of the motor were allegedly seen to exit it.
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After that, a 27-year-old man was tracked down nearby and taken to hospital.
He was later arrested and charged in connection.
Police say he has been released on an undertaking to appear at Glasgow Sheriff Court at a later date.
Meanwhile, an investigation is underway to track down the second person that was in the motor.
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A spokesperson for Police Scotland said: “Around 11.50pm on Wednesday, August 14, 2024 we were made aware of a crash involving a car and two stationary cars on Thornwood Avenue, Glasgow.
“The two occupants were seen to exit the vehicle.
“A 27-year-old man was traced nearby and taken to hospital for treatment.
“He was subsequently arrested and charged in connection and has been released on an undertaking to appear at Glasgow Sheriff Court at a later date.
“Enquires are ongoing to trace the second occupant.”