Police said the father had stepped out of the train for a smoke during its Hamburg stop on Tuesday afternoon.
A police statement issued Wednesday said when the train started moving out of the station with his 9- and 7-year-old children inside, the man allegedly grabbed the pleated rubber cover between two cars and tried to climb his way to a door.
A passenger spotted him and alerted a conductor, who ordered the train halted.
The father faces a criminal investigation.
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