The incident occurred at around 11.30pm on October 17, when British Transpot Police (BTP) were made aware of a man talking loudly about his 'dislike of Muslims' on the 10.52pm Trans Pennine Express service from York to Leeds.
A passenger on board sent a text message to BTP.
The man was white with a shaven head and approximately 5ft 6ins tall and of a slim to medium build.
Officers are appealing for any witnesses who were on board the train and heard what happened, to get in touch. Or, if the description matches someone you know, to get in touch.