The incident occurred on January 10 at Heron Hill in Kendal, where a Black Audi A3 reversed into a Honda Jazz and then drove off at speed without exchanging details.
Police are looking for anyone to identify the car or the woman driving the Audi.
Extensive damage valued at thousands of pounds has been caused to the Honda Jazz.
Anyone with information relating to this incident can report online at www.cumbria.police.uk/reportit , quoting incident number 163 of 18 January 2023. You can also phone on 101.
Alternatively, you can contact Crimestoppers, anonymously, on 0800 555 111.