Officers made the appeal following the terrifying incident on Tuesday, May 24.
At around 6.30pm, a woman was driving at the Hornhill Roundabout, off the M80 roundabout heading towards Kirkintilloch, when a vehicle stopped in front of her.
A man jumped out of his a grey Audi RS5 and banged on the window of her car, shouting and swearing.
He then followed the woman in his vehicle along Initiative Road, Easter Garngaber Road and then onto Kirkintilloch Road in Lenzie, ending near to Kirkintilloch Police Office.
Police said the woman was shaken but unhurt by the incident.
Police Constable Adams of Kirkintilloch Police Station said: “We are appealing for anyone who witnessed the incident to come forward. The car in question was a grey Audi RS5.
“This is a very busy road, so there would have been a lot of drivers around. I would ask anyone in the area around the time of the incident, particularly those with dash cam footage to contact us.
"Any small piece of information could assist in our enquiries.”
Anyone with any information is asked to call Police Scotland via 101, quoting incident number 2982 of Tuesday, 24, May, 2022. Alternatively, please call Crimestoppers on 0800 555 111 where information can be given anonymously.