It happened at the junction of Glumangate and Saltergate at 12.50pm on February 24 but police have only released the details today.
It involved a 72-year-old female pedestrian and a grey VW Polo.
The woman, who was understood to be crossing the road at the time of the collision, required hospital treatment for serious injuries.
The driver of the Polo, another 72-year-old woman, was uninjured.
Since the collision, police say they have been following a number of lines of enquiry and are appealing for witnesses as a next step.
Anyone with information is asked to contact PC Reece Smith-Tyler of Derbyshire Constabulary, quoting reference number 22*110878.
You can also call Crimestoppers anonymously on 0800 555 111.
If you have footage that may be useful for officers, please ensure it is securely downloaded to another device and kept safely for them to view.