The alleged incident happened between the two cities between 9am and 9.44am, and the train was met by police at Glasgow Queen Street station.
They took the details of one man in connection with the alleged offence, and are now appealing for witnesses to get in touch “to understand what happened and who was responsible”.
At Glasgow Queen Street the train was met by BTP officers and they spoke and took the details of a man in connection.
Anyone with information is asked to contact British Transport Police by sending a text to 61016 or call 0800 40 50 40 quoting reference 168 of 11/03/2018. Alternatively, ring Crimestoppers anonymously on 0800 555 111.