Police said no arrests had yet been made in connection with the death of Freda Walker.
Mrs Walker's widower, Shirebrook Town Council member Ken, aged 88, was found with life-threatening injuries after paramedics were called to the couple’s home on Station Road, early on Saturday.
He is currently in a critical condition in hospital, police said.
Speaking at the scene today, Assistant Chief Constable Dave Kirby, of Derbyshire Police, said: “On Saturday, January 15, at 9.30am, police were called by paramedics to this address on Station Road, reporting that two people had been seriously injured, one man and one woman.
“Eighty-six-year-old Freda Walker was pronounced dead at the scene and 88-year-old Kenneth Walker was found to be seriously injured. He is currently in hospital in a critical condition.
“Freda was killed and Ken was left for dead, and we will be asking for your help in identifying who was responsible.
“The family of Ken and Freda have been informed and they are being supported by specially trained officers, but I would ask that their privacy be respected at this time.”
Confirming no arrests had been made in connection with the incident, Mr Kirby said: “Officers remain here at the scene and they will remain here for some time while the investigation is progressed and while forensic examinations are carried out.
“At this time, we haven't made any arrests. However, we can say we are not treating this as a domestic incident.
“There are several lines of inquiry being followed and one of those is that this may have been a burglary but of course, we are keeping an open mind.
“Understandably, this is a horrendous incident for the local community and our thoughts are with everybody who is affected, but particularly with the friends and family of Ken and Freda.”
“I would like to reassure the community that every necessary resource from the force and from the regional East Midlands special operations unit are working together 24 hours a day to find out who is responsible and to establish the full facts of what happened.”
Addressing whether links had been made to other offences in the area, Mr Kirby said: “We are, of course, looking at any incidents which might be linked to this tragic incident, and looking at how we can tie those investigations together.
“However, at this time, we haven't formally linked any other incidents.
“The person responsible for this crime has not yet been apprehended, that said, we don't believe that there's currently any ongoing threat in this local area specifically.
“Our advice would always be to keep doors and windows secure as a general crime prevention policy.”