The authority is treating the incident, which happened at Sandal and Agbrigg railway station on Saturday September 7 shortly before 7pm, as trespassing.
The male youth, who was with two others, was captured on footage jumping down onto the tracks from platform one at the station then crossing the tracks.
-He then stood on the track for a short time before jumping out of the way of a train when it travelled through the station.
PC Sam Bloomfield said: “This was reckless and completely irresponsible behaviour, the person in the footage was dicing with death.
“The driver of the train, a Virgin East Coast service which was not scheduled to stop at the station and was travelling through at speed, was forced to apply the emergency brakes and narrowly avoided hitting the boy, who jumped up onto platform two.
“Trespassing on the railways can cause millions of pounds worth of damage and puts lives in danger. It’s vital that we speak to the youth in the footage, who was wearing a distinctive red and blue T-shirt with the words ROSS or BOSS written in white across the chest, so we can make the aware of the potential consequences of their dangerous behaviour. If you recognise him then please contact us.”
Anyone with information is asked to contact British Transport Police on 0800 40 50 40, or text 61016, quoting reference P-SUB/B3 of September 30.
Information can also be passed anonymously to the independent charity Crimestoppers on 0800 555 111.