A police constable with 28 years' service remains in custody after being arrested on suspicion of murdering his wife.
Northamptonshire Police named Pc Otis Goldsmith as the 49-year-old male who was yesterday arrested just after 1pm after officers were called to a home address in Wootton Hall Park, Northampton.
Superintendent Chris Hillery said people had been left "shocked and upset" by the crime, and offered his condolences to the victim's family and friends.
The force also confirmed that Pc Goldsmith was off-duty at the time of his arrest.
The investigation into what happened is being run through the East Midlands Special Operations Unit, however Northamptonshire Police has stressed none of its own staff will be involved in those inquiries.
The force has also separately referred the incident to the Independent Police Complaints Commission, as the incident involved a serving officer and a death.
"I would like to offer mine and Northamptonshire Police's condolences to the family and friends of the victim of this incident," said Mr Hillery.
"We were called to a private address at Wootton Hall Park just after 1pm yesterday and arrested a 49-year-old man on suspicion of murder.
"I can now confirm the man arrested is police constable Otis Goldsmith, an off-duty officer from Northamptonshire Police.
"Otis Goldsmith is currently in custody in Northampton being questioned by detectives."
He added: "Mr Goldsmith has served with Northamptonshire Police for more than 28 years.
"What has happened has understandably shocked and upset many people within the local community and again, I would like to offer our sincere condolences to all those affected."
Around 50 officers are working on the case drawn from forces in Nottinghamshire, Leicestershire, Lincolnshire and Derbyshire.
A post-mortem examination was due to be carried out by a Home Office pathologist at Leicester Royal Infirmary.
Meanwhile, police have appealed for anyone with information about the incident to call 101 or contact Crimestoppers anonymously on 0800 555111.