The incident took place late Sunday at the Cantt road when officer Varun Singh was driving back in motorcycle for night duty.
According to police, the officer was crossing Khandari road when a speeding UP Roadways bus hit him from the front. He was dragged for a few metres.
The officer was rushed to the Balrampur hospital. He was referred to the Trauma Center because of severe loss of blood and "critical head injury", police said.
He is still critical, said the attending doctors.
Police are on a lookout for the absconding driver and the conductor.
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