The body of the woman, who was in her 50s, was found in Letterkenny, Co Donegal on Saturday morning.
The remains of the woman, who is originally from the Fanad area of Donegal, were removed to Letterkenny General Hospital after a forensic examination.
Garda Superintendent Eugene McGovern said that an autopsy on the woman’s body would be carried out today.
“The forensic examination is now done and dusted and the body has been removed to Letterkenny General Hospital,” said Supt McGovern.
“We cannot comment on the cause of death at present until the local pathologist carries out a post mortem on Monday.”
Locals at Lower Main St, where the body was discovered, expressed their shock and sympathy at the death.
It is understood that the woman, who was a widow, had been living in the apartment for a number of months.
It is understood the woman’s husband was killed in a car crash a number of years ago.