Man in his 70s was airlifted to hospital with head and chest injuries.
The boat put out a mayday after it began taking on water in the north-west Highlands.
When officers arrived at the crash site in Midlothian, no one was in the car.
The CHC S92 was on its way to an offshore platform when it was forced to stop in Shetland.
HM Coastguard launched an overnight search for the man who was later found onshore.
The 55-year-old disappeared after getting into difficulties near Cardwell Bay on Saturday night.