The incident happened on the A917 between Elie and St Monans and is thought to have taken place between 7.30pm and 7.45pm last night
Members of the public contacted police after finding the 43-year-old male cyclist lying on the roadway, having sustained a significant head injury.
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He was taken to Ninewells Hospital where he remains in a critical condition.
Road Policing Officers attended along with other divisional resources and the road was closed until 4am on Tuesday July 9.
While officers are keeping an open mind, inquiries are focusing on whether the man may have been struck by a vehicle, which then failed to stop.
Detective Chief Inspector John Anderson from Fife CID said: “The male cyclist has sustained serious head injuries and we are actively working to establish if a motorist was involved and did not stop after the incident took place.
“Given the time of day this occurred, it is unlikely any individual would be unaware of they had struck someone, as there would still have been plenty of light.
“I would ask any motorist involved to search their conscience and come forward as a matter of urgency to speak with us and explain the full circumstances of what happened.
“Specifically I am also looking to speak with the driver of a silver Vauxhall motor vehicle that we know sustained damage on the Elie to St Monans road near to Ardross Cottages.
“Likewise, any other motorists or members of the public who have any relevant information, including anyone with dash-cam footage who may have been travelling in this area of Fife yesterday evening, should also contact police immediately.”
Those with information can contact Police Scotland via 101 and quote incident number 3910 of the July 8. Alternatively, an anonymous report can be made to the charity Crimestoppers on 0800 555 111.
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