It happened on Saturday, March 9 at about 11.45pm.
A man sitting next to two women on the train began to speak to them.
The conversation turned heated and he assaulted one of them from across the table.
They then moved to sit somewhere else.
The girls were travelling from Manchester Victoria to Halifax station.
A man has been identified and is helping police with their enquiries.
However, officers are keen to trace three women he was speaking to before the altercation.
The British Transport Police have asked the women or any witnesses to contact them by texting 61016 or calling 0800 40 50 40 quoting reference 217 of 27/03/19.