The incident, involving a grey Audi A3, happened in Sandy Lane, Bearsted at 4.30pm on Monday 11 April 2022.
It is alleged the Audi was travelling the wrong way along the one-way street, when its wing mirror struck a woman as she tried to get onto a verge.
The victim, who is in her 70s, suffered minor injuries and did not require hospital treatment.
Officers are now trying to identify the driver and would like to hear from anybody who may have seen a grey Audi A3 in the Bearsted area, at around the time of the incident.
Can you help?
Motorists with dashcam or residents with private CCTV are also asked to check for footage that may assist the investigation.
Anyone with information is urged to call Kent Police on 01622 604100, quoting reference 46/67541/22.