The 64-year-old was found on the B961 between Monikie and Newbigging shortly before 10.45am on Friday, April 14 , having come off his grey mountain bike.
He was taken to Ninewells Hospital in Dundee for treatment.
Sergeant Brian McEwen said: “Our enquiries continue to establish the full circumstances which led to the man coming off his bicycle.
“He was found by members of the public who administered first aid before the ambulance arrived.
“The man had been cycling south on the road before the incident and I would urge anyone who may have seen him or who has any dashcam footage to come forward if you haven’t already spoken to an officer.
“Anyone who can help is asked to call 101, quoting reference 0908 of April 14.”