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.
More top news
A woman died during scenes of panic at a Kenyan university after police carried out a terror drill without the students being told first.
The Prince of Wales said world companies 'pay no attention' to the damage their supply chains cause to forests.
Investigators say a faulty rudder system and the pilots' responses contributed to an AirAsia jet crash last year which killed 162 people.