Fire crews and an ambulance were called to the house in The Paddock, Elwick, at 5.45am on Friday where they found the woman inside the house.
Tributes to blaze victim nurseShe was treated for severe smoke inhalation at the scene.
The woman was taken to the University Hospital of Hartlepool where she died a short time later.
A post-mortem examination took place yesterday afternoon and she was formally identified by relatives this morning.
Detective Superintendent Gordon Lang, in charge of the investigation, said: "Our sympathies go out to Mrs Cutter's family and friends who are obviously devastated by their loss.
"Investigations into the cause of the fire are continuing. I would urge anyone with information to come forward."
Anyone with information regarding the incident should contact Hartlepool Police on (01642) 302126 or Crimestoppers anonymously on (0800) 555 111.
Meanwhile, people living in the leafy village today told of their shock at the death.
Neighbours and residents in the area said they cannot believe what has happened.
One neighbour, who did not wish to be named, said: "I can't believe it, it is just terrible.
"I woke up and smelled smoke and rang the fire brigade.
"I don't know the woman, I just knew her to say 'hello' to and if the couple were in the garden I would speak to them.
"I think they had a dog because I used to see them out walking."
Residents said the woman lived with her husband after moving in around 18 months ago.
Another neighbour, who lives in The Paddock, said the house had been up for sale since before Christmas.
She added: "They just kept themselves to themselves really. It is quite a quiet street so I didn't really speak to them very much.
"It is shocking what has happened, I just can't believe it."
Police were continuing to carry out investigations in the area and forensic experts were seen carrying out tests nearby.
Cleveland Fire Brigade were called to the property at around 5.45am yesterday to reports of a fire.
The woman was found in bed in one of the upstairs rooms.
Flames had burned through the staircase at the property and firefighters had to use a ladder to get upstairs.
Firefighters believe the fire had started on the ground floor.
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