A Facebook message states that a cyclist was taken to hospital 'in a bad way' after being hit by a car on Harpur Hill Road on Sunday afternoon.
The message, which has been shared more than 200 times on the social networking site, adds: "If anyone knows who did it or knows any details, please own up."
A Derbyshire police spokesman said: "We have spoken to the cyclist, who is a 43-year-old man from Buxton.
"He’s still in hospital being treated for multiple fractures and grazes.
"He was riding down Harpur Hill Road at about 4pm on Sunday when he came off his bike.
"It’s unclear how the crash happened but he alleges that a car clipped his back wheel.
"One witness has come forward but if anyone else was in the area we’d be pleased to hear from them.
"Anyone with any information or anyone who saw anything at the time should call police on 101, quoting incident 614 of May 22."