Police were called by the ambulance service to reports of a woman's body at an address on Soaper Lane, Shelf at 844pm on Saturday 2 April.
Officers attended and found the body of an adult woman.
Enquiries into the incident remain ongoing and the death is currently being treated as suspicious. A 34-year-old man has been arrested in connection with the incident and remains in police custody.
Senior Investigating Officer, Detective Chief Inspector Warren Stevenson, said:
"This investigation is at an early stage and I am trying to find out exactly what happened. I would appeal for any witnesses or anyone with information to contact police on 101."
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