The driver sped through the level crossing before the barriers came down, but reversed through the barrier and stopped in the middle of the tracks.
The "extremely dangerous" example of driving was captured on CCTV.
It happened at Pinxton level crossing, on the Nottinghamshire and Derbyshire border, at 00:30 BST on Sunday 21 June.
Insp Anton Menzies from British Transport Police hopes someone will recognise the distinctive three-wheeled car from the video.
"This was extremely dangerous behaviour that put the driver and the passengers' lives at risk," he said.
"They were very lucky that a train was not coming through at the time or the consequences would be unthinkable."
The video shows a passenger getting out of the car while it is on the crossing.
Another person lifts the barrier, allowing the car to drive away.
The barriers were damaged by the car and will cost up to Â£15,000 to repair.
Police are trying to identify a Reliant Robin driver who inexplicably reversed on to a level crossing.