Officers riding off-road bikes chased the man who was on an off-road moped after he failed to stop shortly before 4.45pm yesterday (June 6), Greater Manchester Police (GMP) said.
The man came off the bike in Shuttle Street, Tyldesley and was taken to hospital in a critical condition, the force added.
Police were taking part in an anti-social behaviour operation at the time.
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The incident has been referred to the Independent Office for Police Conduct, GMP said.
Pc John Cavanagh, from GMP’s serious investigation collision unit, said: "Our thoughts are with the man’s family who are understandably distressed whilst he fights for his life in hospital.
"A cordon is currently in place at the scene and we have referred the incident to the IOPC due to the police contact in the moments before this incident.
"We will do all we can to support any subsequent investigation."
Anyone with information can report it online or by using GMP’s LiveChat service online at www.gmp.police.uk quoting incident number 2138 of 06/06/2021.
Alternatively, people can contact Crimestoppers anonymously on 0800 555 111.
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