The 40-year-old man is being interviewed by police after answering a phone which had been used to call triple zero.
Raised voices could be heard in the background during the first triple-zero call about 11.45pm on Wednesday, but nothing was said to the dispatcher, police said.
They called back and spoke to the man who answered, telling him police would attend after he provided his name and address.
Another call was made to triple zero almost two hours later at 1.40am on Thursday when someone in the street saw a woman dangling from a balcony on the seventh floor of the unit block.
Police were by then on their way and arrived about a minute later to find the woman with critical injuries outside the unit block on River Rd at Parramatta in Sydney's west, Detective Superintendent Barry Vincent told reporters on Thursday.
"Whether she was trying to hold on ... that will form part of our lines of inquiry, obviously how she came to be there is a key factor," Det Supt Vincent added.
The woman, believed to be aged 39, was pronounced dead at the scene after unsuccessful attempts to revive her.
She is yet to be formally identified.
Uniformed officers were seen canvassing residents as they left and arrived at the apartment tower on Thursday morning.
Forensic investigators were later seen leaving the building as the unit was examined.
Police have been told the woman fell from a seventh-floor balcony. (Dan Himbrechts/AAP PHOTOS)
The man in custody has not been charged with any offence.
He lives at the address, however the woman is believed to have a different residence.
The pair were believed to have previously been in a domestic relationship, but it was not yet clear if they were still in a relationship at the time, Det Supt Vincent said.
The phone initially used to call emergency services was not registered in the name of the man who answered it but it was believed he used it, with police investigating whether or not he initiated the first call which did not involve a direct interaction.
Uniformed police have been speaking with residents. (Dan Himbrechts/AAP PHOTOS)
An apprehended violence order had been in place for the man's protection, Det Supt Vincent said.
The woman has not been formally identified and police are not yet able to confirm whether she was named in the order, or if any orders were in place protecting her.
Police are continuing to interview the man as investigators process a crime scene at the apartment block.
Anyone with information about the incident is being urged to contact Crime Stoppers.
