The 54-year-old man, of Leicester, was arrested on Saturday (17th April).
At around 10.30am on Thursday (15 April) officers attended a property in Tennis Court Drive following concern for the welfare of the occupant inside.
Entry was gained to the address and the woman, 49, was pronounced dead at the scene and an investigation was launched.
A post mortem examination concluded she died as a result of a head injury.
As part of the investigation, officers continue to carry out enquiries following an incident that took place in Norfolk the same morning.
A man, in his 50s, was found on a beach in Hunstanton with life-threatening injuries after it is believed he fell from the cliffs. He remains in hospital in a serious condition.
A scene preservation which was in place in Tennis Court Drive to allow for a forensic examination of the scene has since been removed.
Specialist officers continue to support the family following her death.
Detective Chief Inspector Joe Banfield from East Midlands Special Operations Unit (EMSOU) is leading the investigation.
He said: “Although an arrest has been made our investigation continues to determine the exact circumstances surrounding the death.
“I would still like to hear from anyone who may have any information related to this incident.
“If you think you can help and have not yet spoken to police I would urge you to get in touch.”
Anyone with information is asked to contact police on 101 quoting incident 127 of 15 April.