Police have identified the woman shot dead in her Seacliff home on Tuesday.
She was Sharon Diane Comerford (54).
The man at the centre of an investigation into her death remains in intensive care in Dunedin Hospital with serious gun shot injuries.
Detective Senior Sergeant Malcolm Inglis, of Dunedin, confirmed police were investigating whether the man was responsible for Ms Comerford's death.
Ms Comerford died from a single gunshot wound, he said.
"We've got to look and prove evidentially he was responsible for her murder.''
Det Snr Sgt Inglis said police were keeping an open mind in the investigation.
The woman was found dead in her Coast Rd home when armed police stormed the building on Tuesday morning.
Officers were earlier called to the nearby Truby King Reserve where they found a critically injured 59-year-old man and a firearm.
He would not comment on whether any charges would be laid.
