Three special constables pursued a car before a passenger jumped out and was killed when he ran into the path of a train, the police watchdog has said.
The Metropolitan Police officers are being investigated over the death of Mircea Adam at a level crossing in Enfield, north London.
Mr Adam, 20, was in a car the officers wanted to check had valid insurance.
The Independent Police Complaints Commission said it would examine whether their actions were appropriate.
The watchdog said it would also assess whether police guidelines had been followed.
The Independent Police Complaints Commission (IPCC) said CCTV footage showed the marked police car was 20ft (6m) behind the Mercedes when Mr Adam was hit.
However, because officers had been following the car for about 90 seconds, several minutes earlier, the IPCC said it had decided to independently investigate the actions of the officers.
The IPCC said the officers acted after carrying out a vehicle check on the car that Mr Adam, also known as Bobi Rostas, was travelling in.
Lights and siren
Wanting to check if the driver was insured they pulled the car over.
When the driver, who initially stepped out of the car, got back in and drove off, the officers activated the blue lights and siren.
The Mercedes pulled away from police before stopping at Enfield Lock level crossing where the barriers were down.
Mr Adam and the driver got out, leapt over the barriers and ran across the tracks.
The driver escaped unharmed and was arrested along with a third man. They have since been released on bail.
Mr Adam, of Rochestown, County Cork, in the Republic of Ireland, was hit by a north-bound train and killed.