Bills' Orakei home was gutted by fire on November 24, 2012.
The 65-year-old grandmother was in the house and neighbours braved the inferno to rescue her from an upstairs room.
It is understood police were considering the possibility Bills was intentionally poisoned at Middlemore Hospital where she was taken after the fire.
Heather Bill's sister, Barbara Henderson, this week declined to speculate on her sister's death until the findings were released.
"I don't know what has happened. It would be foolish to make that prediction because I am not a doctor and I don't have all the medical records at my fingertips," she said.
"I believe they will know next week if they will investigate further."
Henderson said she would be waiting to hear what police had uncovered through the tests.
"If the findings are that this is not through natural consequences, then that is a different category altogether," she said.
"If it is not natural causes, the police are going to take it further and we have to let them do their job. That is the way it is."
Henderson said she and other family members were by her sister's side when she died.
Detective Inspector Dave Lynch was on annual leave yesterday and could not be reached for comment.
Last year he said associates of the deceased and medical staff had been interviewed as part of the investigation.
He said police were keeping an open mind on how Bills died and whether the cause was sudden but natural, or something more sinister.
Lynch said if forensic results raised suspicions, police would have to establish whether anyone else was involved in a criminal capacity.
Middlemore Hospital spokeswoman Lauren Young said yesterday it was inappropriate to comment as the police investigation into Bills' death was ongoing.
Young said there would be no comment "until the police have made a decision on whether there is a case to answer or not".
