Shortly before 11.30am on Sunday 18 July, a silver BMW 3 Series failed to stop for officers when requested to do so in Military Road.
The car was then driven along Sandgate High Street and Sandgate Esplanade before it was stopped by police in Naildown Road, Hythe.
A 19-year-old man was arrested in connection with the incident and remains under investigation.
Enquiries are ongoing and anyone who saw the vehicle driving dangerously in the area or who has dashcam or CCTV footage which may assist is urged to call 01843 222289, quoting reference 18-0541.
You can also contact Crimestoppers in Kent anonymously by calling 0800 555111 or by filling in the online report form.