In a statement Emma's family said: "She was our much-loved daughter and a baby sister. This tragic incident has left us shocked and devastated."
Read the statement in full here.
British Transport Police has said its investigation is in its early stages. Officers are working out how the car came to be on the tracks.
In a statement issued through British Transport Police, Emma's parents, Mark and Zoe Lifsey, said:
In a statement, the Brititish Transport Police said:
"A four-year-old girl, Emma Lifsey, sustained serious injuries and was airlifted to Sheffield Children's Hospital, where she was sadly pronounced dead in the early hours Wednesday, 5 December. Her family have been notified.
"The police investigation into the incident is ongoing and remains very much in the early stages. Officers are working hard to establish the full circumstances surrounding the incident, including how the vehicle came to be on the tracks at the time."
A four-year-old girl is in a serious condition in hospital after the car she was in collided with a train on a railway crossing.
The child was airlifted to hospital in Sheffield and is in intensive care following the incident yesterday in north Nottinghamshire.
The driver, a 67-year-old woman, was taken to hospital in nearby Doncaster with neck injuries and bruising.
Two women and a child have been seriously injured after the car they were travelling in was hit by a train at a level crossing in South Yorkshire.
British Transport Police said the child has been airlifted to hospital.