The crash happened around 7:20 a.m. on Howard Street between Miller Avenue and 6th Place.
Three victims were ejected from a silver Chevrolet sedan and were pronounced dead at the scene, Gary police Commander Jack Hamady said.
The victims were identified as Deniya Brown, 11, Deyki Mitchell, 13, and Shermika Herbert, 37, according to the Lake County coroner’s office. They lived in Gary.
Gary Mayor Jerome A. Prince said the incident was "especially painful" because the victims were from the same family.
"We lost several members of a family in a train-car collision this morning. At this point, details are limited as different law enforcement agencies and the CSX railroad continue investigating this incident," Prince said in an emailed statement.
"Whatever the outcomes of these investigations, I implore every resident and visitor to be extra cautious when using every railroad crossing and please respect crossing gates and safety devices throughout our city," he said.
CSX train police are investigating along with Gary police.
Sun-Times Media Wire contributed to this report.