Justine Damond, 40, was gunned down on Saturday after calling police to report a possible crime in her quiet Minneapolis neighbourhood.
State investigators say the officers whom she encountered failed to activate their body or dashboard cameras.
Every police officer and squad car in Minneapolis is equipped with cameras.
"I have the same questions everyone else does. Why weren't the police cameras on?" said mayor Betsy Hodges on Tuesday.
Minneapolis police are required to switch on their body cameras only during certain encounters, unlike in Los Angeles or Washington DC, where cameras must be switched on for any response to a call for service.
Instead, there are more than a dozen situations in which cameras should be used, according to the police manual, which adds that failure to use the camera could result in job termination.
"If a BWC [body-worn camera] is not activated prior to a use of force, it shall be activated as soon as it is safe to do so," reads the manual.
Local media reported that Ms Damond was dressed in her pyjamas and had approached the driver's side door to talk to the officer at the wheel after police arrived.
Officer Mohamed Noor, who was sitting in the passenger seat, fired his weapon across his partner and through the driver's door, striking Ms Damond in the abdomen.
Her fiancé, Don Damond, said on Monday that the family is "desperate" for answers from officials.
Speaking in Sydney, her father John Ruszczyk said: "Justine was a beacon to all of us, we only ask that the light of justice shine down on the circumstances of her death."
Hennepin County Attorney Mike Freeman says he will personally decide whether to charge Officer Mohamed Noor, rather than put the question to a grand jury. And he also questioned why the cameras were not turned on.
Officer Noor, who has been described by local media as a Somali-American, has been with the police force for two years.
A statement from his lawyer said he had arrived in the US "at a young age" and described him as "a caring person with a family he loves and he empathised with the loss others are experiencing".
But KSTP-TV, citing city records, reports that in two years of policing the officer had attracted three formal complaints, two of which remain unresolved.
Sources say his partner who was at the scene is Matthew Harrity, 25, who joined the force last year.
Ms Damond's death has made headlines across her native Australia.
The Australian: "Justine Damond and Mohamed Noor were two strangers from distant lands who arrived in America to fulfil their dreams, but in a tragic meeting in a Minneapolis alley one was killed and the other could face serious criminal charges."
The Sydney Morning Herald: "The 40-year-old's family and wide network of friends on Sydney's northern beaches have been left reeling. They struggle to comprehend how Ms Damond became a victim in America's ongoing and controversial police shootings."
The Age: "The scale of the deaths [of people at the hands of police in the US] is simply unimaginable in many other countries around the world... The high ownership of guns and prevalence of gun crime in America means American cops operate in completely different and more violent circumstances to their Australian counterparts."
A police radio recording from the incident was released on Tuesday, in which officers at the scene can be heard telling dispatchers they are performing CPR, and that "no suspects are at large".
Minneapolis Police Chief Janee Harteau called Ms Damond's death "tragic" in a statement on Monday.
"I've asked for the investigation to be expedited to provide transparency and to answer as many questions as quickly as we can," she said in her first comments on the killing.
The two officers involved in the shooting are on paid administrative leave.
Ms Damond, nee Justine Ruszczyk, studied to be a veterinarian before relocating from Sydney to the US, where she is believed to have been for at least the last three years.
According to her website, she was a "qualified yoga instructor, a personal health and life coach and meditation teacher".
Over the past few years the US has seen a series of civilian killings at the hands of police that have prompted a national debate.
Questions are being raised by officials about why a police officer who shot an Australian woman and his partner did not record the fatal incident.