Two women were running along Dock Road shortly after 8.10pm on Wednesday (8 November).
They were then in collision with a vehicle at the junction with Marshfoot Road and Old Dock Approach Road.
The car – believed to be a dark-coloured BMW – failed to stop at the scene of the collision, making off along Old Dock Approach Road towards the B149 Wood View.
As the car left the scene at speed, it overtook another, smaller car which we believe is a Ford Fiesta.
We also want to trace the driver of this car and speak to them as a witness.
Detective Sergeant Steve Holmes said: “Two people have sustained really serious injuries as a result of this collision and it’s really important we’re able to find the driver involved.
“I know these images are not the clearest, but I hope releasing them will trigger someone’s memory.
“I believe the impact of the collision will have left the car involved with damage to it and this would be visible.
“Has a neighbour returned home with damage to their car that wasn’t there in before?
“Have they parked their car differently to how they usually do?