Police said the car that rammed the e-bike had pursued the bikes through the village of Pleasley, with the last known sighting of it in Rowthorne Lane, where it turned right on to the A617 towards New Houghton.
A man was driving the vehicle, with a woman in the passenger seat, the force added.
Officers want to hear from people who might have seen a Land Rover Discovery, thought to have been manufactured between 2004 and 2009, in and around the Pleasley area around the time of the crash.
The force said the woman it wants to speak to was pictured outside The White Swan in Meden Square, Pleasley, shortly before 20:00 on Tuesday.
She is believed to have “vital information” about the incident, it said.
