Officers were called out to the station around 3pm following reports of the attack, believed to have happened on the railway overbridge.
Witnesses on social media sites spoke of “a large police presence” at the station.
Transport police told the Herald they attended the scene with colleagues from Police Scotland but said no parties involved in the “altercation” could be found.
At the same time, Scotrail advised passengers not to use the railway bridge at the station.
In a message on Twitter, Scotrail posted: “Passengers on services from Dalmuir/Milngavie travelling to Westerton who require to cross the overbridge should alight at Anniesland and travel back from there to Westerton."
Police said enquiries into this incident are ongoing and no arrests have been made in connection with it.
The overbridge was closed for several hours after the incident.
Witnesses or anyone with information are urged to contact BTP by texting 61016 or calling 0800 40 50 40 quoting reference 317 of 14/12/21.