British Transport Police officers are seeking witnesses after a group of passengers sang sectarian songs on a train travelling between Edinburgh and Dunblane on Saturday, September 13.
Another passenger travelling on the train was spat on during the journey.
The group of between six and eight men, all aged in their 40s, left the train at Larbert station, on the 8.35pm service.
Constable Jonathan Harvey, the British Transport Police officer in charge of the enquiry, is appealing for witnesses to come forward.
He said: “This sort of behaviour is unacceptable and passengers and rail staff should be able to travel without encountering it.
“Anyone who was on the 8.35pm Edinburgh to Dunblane service or at any of the stations en route and who has information which could assist officers with the inquiry should contact British Transport Police as a matter of urgency.”
British Transport Police can be contacted on 0800 40 50 40 or by texting 61016.
Information can also be given anonymously to the independent charity Crimestoppers on 0800 555 111.