A woman thought to have been shot by her husband before he turned the gun on himself was originally from Corby.
Police believe North Norfolk District Council leader Keith Johnson, 58, killed his wife Andrea, 44, with a shotgun before killing himself.
They are investigating possible motives including aspects of the couple’s personal lives.
A statement from Mrs Johnson’s family said they are devastated by the loss of their beautiful daughter Andrea, a wonderful daughter, aunt and sister.
It went on: “She was so bubbly and full of life, she adored her family and has been tragically taken from us. She will be very sorely missed. Please leave us to grieve in peace at this sad time.”
Today (Thursday, December 6) Norfolk coroner William Armstrong opened and adjourned an inquest into the deaths.
He said a post-mortem examination found Mrs Johnson, formerly Chadwick, a customer services representative originally from Corby, was shot in the chest.
She was found in a neighbour’s front garden and paramedics could not resuscitate her, Mr Armstrong said.
Mr Johnson, originally from Sheringham, was found in the back garden of the couple’s home in Roughton, near Cromer, with a gunshot wound to the neck.
Police believe he used one of four shotguns registered to his wife.
Mr Armstrong said: “It is unlikely there will be any criminal prosecution arising out of this but these matters are now subject to a police investigation on behalf of the coroner.”
The couple were found dead at 2.50pm on Sunday when police were called to their house in Compit Hills after reports of gunshots.
A full inquest will be held at a later date.