Officers were called to Writtle, near Chelmsford, at 8.45am after a member of the public reported hearing a single gunshot.
Eyewitnesses said officers sealed off the grounds of All Saints Church and turned back parents taking their children to school via the path.
At a press conference later police confirmed Reeve's death and said no shots were fired by police.
It's believed Reeve had some "strong connection" to the village and the church where he took his own life.
He was "largely unknown" to police who are investigating how he got a gun and what triggered the incident in Clacton which cost Pc Dibell his life while off duty.