Police were called by the ambulance service to an address in Cheltenham earlier today with a report that a woman in her 40s had sustained injuries.
The call was made toat around 9.35am with officers subsequently attending an address in Salamanca Road in the Whaddon area.
A woman inside the property was pronounced deceased by paramedics.
A man was later arrested on suspicion of murder and is in police custody.
Investigating officers are appealing for witnesses of a black Vauxhall Corsa driving erratically in the Cheltenham area this morning in connection with the incident.
Scene guards are in place and the investigation is in the early stages.
At this time police are not currently looking for any other suspects and those involved are known to each other.
The woman’s next of kin have been informed and are being supported by specially trained officers.
Anyone with information which could assist the investigation and who has not already spoken to police is asked to provide information online by competing the following form and quoting incident 105 of 15 March:
They can also call police on 101.