Merseyside Police have referred to the tragic incident on Scotland Road near the Wallasey Tunnel in Liverpool to the Independent Office for Police Conduct
Police reported the incident to the police watchdog, the Independent Office for Police Conduct (IOPC).
The man – who has yet to be identified – was knocked down on Scotland Road at around 18:50 GMT and was later pronounced dead in hospital.
Witnesses say that the police vehicle had its flashing blue lights on and the victim while he was crossing the road and then the collision occurred.
An IOPC spokesman said investigators had assessed the scene and decided to carry out an independent investigation.
Scotland Road was closed following the incident, which Mersey travel said also prompted the closure of the Bottle-bound slip road from the Wallasey Tunnel.
In a statement, Merseyside Police said: "Emergency services attended and the pedestrian was taken to hospital where he was sadly pronounced dead.
"Enquiries are ongoing to identify him and inform his next of kin."