Police said detectives from the serious collision investigation unit have been at the scene since the crash, gathering evidence to establish what happened.
The A46 was closed in both directions and has since reopened.
Det Con Madeleine Hayes said it was a “tragic incident with three people losing their lives” and appealed for information.
“We know the car was travelling on the A46 from Nottingham,” she said.
“We are working to understand what led the car to leave the carriageway and any information from witnesses may be helpful in establishing this.”
Det Con Hayes asked people to view their dashcam footage from between 00:30 and 01:05 and contact police with any information.