French police are convinced there has been a murder. The problem is, not only is there no corpse, but no-one has even been reported missing, reports BBC News.
In a mystery straight out of an Inspector Maigret novel, Normandy's state prosecutor has appealed to the public to help discover who it is that might be dead.
"In my 23 years as a magistrate, I have never seen a situation like this," said Rémi Coutin.
"We don't have a body," he said.
"And we don't have an identity for the person who we believe to have been killed."
What police do have is a suspect. He is a 46-year-old Polish man who has lived in France for many years, working as a carpenter. The unnamed man is currently in custody.
Police think that on 9 March, the suspect, driving a black Audi under the influence of alcohol, knocked over a woman cyclist on a road near the town of Grand Bourgtheroulde, 140km (85 miles) north-west of Paris.
Thinking he had killed her, he went home to get a spade. But when he came back, he found she was still alive. So the police believe he "finished her off" with the spade, then buried her body. The bicycle he disposed of at a rubbish dump.
There is precious little material evidence that any of this actually took place. There is no body, no confession to police, no bicycle. Above all, there are no reports of a woman cyclist going missing.
The reason the police are sure that a murder did happen is that the man initially told people who were near to him that he had done it.
On 14 May - more than two months later - the suspect's former girlfriend went to the police station in Dieppe. She told a story about how her ex had phoned her in a drunken state on 9 March, to tell her he had killed a woman in an accident.
That was his initial version.