Former mayor Janette Dunbavand and her husband John were found dead at their Northchurch home in a suspected murder-suicide on Friday morning (March 22).
The bodies of the couple, both 81, were discovered at their cottage just before 8am.
Mrs Dunbavand, who suffered from dementia, had been the mayor of Berkhamsted while her husband was a former Tory councillor.
Hertfordshire Constabulary said it was not looking for anyone else in connection with the deaths.
Stunned neighbours said they heard gunshots early in the morning of the incident.
One said: "It was a complete shock for everyone around here and my wife actually heard the gunshot when our kids were outside playing before school."
Officers were called to the home following concerns for the welfare of the Dunbavands' and they were pronounced dead at the scene.
The circumstances of their deaths were being investigated by police.