UPDATE: The road is now partially blocked due to an oil spillage and earlier accident.
Police have confirmed that a VW Golf was involved, with the car hitting a hedge and rolling onto its roof.
The driver of the car, which is registered to Falmouth, has been taken to hospital following the crash near High Cross.
The Constantine to Treverva road was blocked in both directions due to a collision.
The crash was affecting traffic to and from Falmouth and the village.