The woman found dead at a Northamptonshire Police detective constable’s home has been named as his wife Jill.
Mrs Goldsmith, 49, married her husband, Otis, last year and they lived together at the semi-detached property on the Wootton Hall Park site of Northamptonshire Police’s headquarters.
Otis Goldsmith’s parents Sylvia and Michael, both 81, live in Rushden.
They have expressed their distress at their son’s arrest.
Mrs Goldsmith said: “We don’t know any details about what happened but Otis has been arrested.
“He and Jill only married last year. This is a very difficult time for us all.”
Supt Chris Hillery said the murder had “shocked and upset many people”.
He said: “I would like to offer mine and Northamptonshire Police’s condolences to the family and friends of the victim of this incident.
“Otis 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.”
Supt Hillery said 50 officers were working on the case from all forces in the region – including Nottinghamshire, Leicestershire, Lincolnshire and Derbyshire.
He said the case was referred to the Independent Police Complaints Commission last night because the incident involved a death and a serving officer.
But he said the IPCC will not be conducting the murder investigation itself which, as with all murder investigations in Northamptonshire, is being led by the East Midlands Special Operations Unit.
A post-mortem examination was carried out at 2pm by a Home Office pathologist at Leicester Royal Infirmary.
Anyone who has any information about this incident should contact Northamptonshire Police on 101 or Crimestoppers anonymously on 0800 555 111.