The incident happened the early hours of July 1 in the car park of McDonald’s at Cardigan Fields in Kirkstall.
The male suspect, who was driver of a white Audi A1, and the woman, who was the front seat passenger, got into an altercation with a group of people that were parked up next to them in a black and white taxi.
A West Yorkshire Police spokesman today said: "The male suspect punched a man from the taxi once to the face causing him to lose consciousness momentarily.
"The same suspect has then forcibly removed his car keys from a woman causing serious injuries to her wrist."
Anyone who recognises the man or the woman shown in the CCTV images or who has any with information that could assist the investigation is asked to contact DC 3023 Sam Shukla at Elland Road via 101, quoting crime number 13180320660.
Information can also be passed on anonymously via the independent charity Crimestoppers on 0800 555 111.