The incident happened on Wednesday, 27 August at around 7.45pm on board the Kings Cross to Harrogate service.
Detective Constable Penny Halliwell said: “A 44-year-old woman from Leeds had got up to leave the train and was waiting for it to pull into Leeds station when she felt something on her bottom.
“When she turned around she saw that a man had exposed himself and was rubbing himself on her.
“The woman confronted the man, who ran off down the train, then once it had arrived into Leeds he jumped off and fled.
BTP detectives are today issuing two images of a man they want to speak to in connection with the incident.
DC Halliwell said: “We would like to speak to the man in the images about this incident as we believe he can help with our investigation.
“We treat all incidents of unwanted sexual behaviour very seriously and I would urge anyone who recognises the man to contact us.”
Anyone with information is asked to contactÂ British Transport PoliceÂ onÂ 0800 40 50 40, orÂ text 61016, quoting reference
PSUB/B3 of 2/9/2014. Information can also be passed anonymously to the independent charity Crimestoppers onÂ 0800 555 111.