CCTV shows the group boarding the 6.20pm Glasgow to Lanark service at Bellshill where they are reported to have acted in a rowdy and disorderly manner before leaving the train at Motherwell.
The group of 10–12 boys, aged between 14 and 17, shouted racially offensive remarks and threw objects at a 44-year-old man who was waiting on the platform at Motherwell station, before one of the group spat on a 25-year-old woman.
A fire extinguisher was also taken from the train and discharged around the station.
CCTV will be reviewed in an attempt to identify those involved.
Meanwhile, Detective Constable David Merchant, the BTP officer in charge of the enquiry, is appealing for information.
He said: “This sort of appalling behaviour is unacceptable and I am appealing for anyone who was on the train or at the station and can provide information which can help identify the youths responsible to contact BTP on 0800 40 50 40 or texting 61016.”
Information can also be given anonymously to the independent charity Crimestoppers on 0800 555 111.