The incident occurred in William Street, Derry, in the early hours of 27 December last, but details have just been released.
The woman was knocked unconcious after she was struck by a dark Vauxhall Corsa with a Donegal registration shortly before 2.00am as she was crossing the road close to the roundabout.
Although she was knocked unconscious, the woman was not seriously injured.
A PSNI spokesperson has asked anyone with information about the incident to contact police on 0845 600 8000 or a member of your local Neighbourhood Team directly – details can be found on the PSNI website.
Alternatively, if someone would prefer to provide information without giving their details, they can contact the independent charity Crimestoppers and speak to them anonymously on 0800 555 111.