Harry Kirkham, 15, from Kingstanding, Birmingham, was killed on Wednesday night as he walked out from the Potter's House Christian Fellowship Church.
He was hit by a patrol vehicle as he crossed Sutton New Road in Birmingham with friends.
West Midlands Police said its thoughts were with the boy's family.
On a Facebook page in memory of the teen his mother Dawn Smith wrote: "Sweet dreams angel, always in our hearts. HARRY-JAMES our 15yr old big boy."
The church has not made any comment but it's understood the school boy was a regular there.
In a statement West Midlands Police said the driver of the police car was "traumatised" by the ordeal.
Chief Inspector Neil Hobson said: "No parent should have to lose a child, particularly in such tragic circumstances. This evening our thoughts are with Harry's family following their tragic loss.
"As Harry was hit by a police car, West Midlands Police has informed the Independent Police Complaints Commission, who continue to be updated."