Christine Formosa Rakic, 50, was found dead at her ex-partner’s home in Rooty Hill about 8.30pm on Tuesday after a family member called police concerned about her welfare.
Rakic had died before police arrived.
Superintendent Steve Egginton from NSW Police said Rakic had suffered “significant injuries”.
Her ex-partner Dusan Rakic, also 50, was found with injuries to his arms.
He remains under police guard at Westmead Hospital.
Egginton said Mr Rakic is in a “critical but stable” condition but is in an induced coma.
“We don’t have a lot of information at the moment based on the fact the two people (were) in the house at the time, one is deceased and the other is effectively in a coma,” Egginton said.
He added Mr Rakic has had interactions with police in the past but “not a lot”.
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“There have been some light offences in the past in respect to the gentleman in hospital,” he said.
Neighbours say they heard screaming and running at the property.
“I’ve never seen this happen around here before and I’ve been here for over 40 years,” one said.
A crime scene has been established and investigations are continuing into the circumstances surrounding the incident.
Egginton said one line of inquiry is domestic violence.
”Sadly it looks like this may be the case,” he said.
National Domestic Violence Service: 1800 RESPECT (1800 737 732). If you are in immediate danger call triple zero (000).