MINNEAPOLIS (CNN) -- Justine Ruszczyk's family says they're still grappling with the reality of her death.
In a statement released to CNN affiliate Sky News Australia, Ruszczyk's relatives said they are devastated she was shot and killed by police Saturday, just minutes after trying to report a possible sexual assault to authorities.
"We are still trying to come to terms with this tragedy and we are struggling to understand how and why this could happen," the family said in the statement.
Though investigators say it may be months until the case comes to a close, the family wants to know what happened "as soon as possible" so they can have a sense of closure.
They'll have to wait for answers, but for now, they want her body back home.
"All we want to do is bring Justine home to Australia to farewell her in her hometown among family and friends. In the meantime, we ask that you give us time to grieve in private and to support each other at this very difficult time," the statement said.
Ruszczyk, 40, was originally from Australia but moved to the United States in 2014. She trained as a veterinarian and later became a yoga instructor and life coach and was planning on getting married next month.
A call for justice
Some of the documents in the case have been shared with Ruszczyk's family, City Council member Linea Palmisano said, but some in Australia are demanding answers now.
"It is inexplicable. Our hearts go out to her family," Australian Prime Minister Malcolm Turnbull said on Australian Channel 9's "Today" show Wednesday.
"I mean, how can a woman out in the street in her pajamas seeking assistance from the police be shot like that? It is a shocking killing."
Ruszczyk's father made an emotional plea for justice.
"Justine, our daughter, was so special to us and to so many others," John Ruszczyk told journalists in Australia. "Justine was a beacon to all of us. We only ask that the light of justice shine down on the circumstances of her death.
The emergency calls released by police offer some of the first clues about what may have led police to shoot Ruszczyk.
Ruszczyk made two 911 calls Saturday night to report a possible sexual assault near her home, according to transcripts released by the city Wednesday.
"I can hear someone out the back and I, I'm not sure if she's having sex or being raped," Ruszczyk said in the first call.
"... And I think she just yelled out 'help,' but it's difficult. The sound has been going on for a while, but I think, I don't think she's enjoying it," Ruszczyk said.
The dispatcher told her police would be there soon.
Eight minutes later, Ruszczyk called 911 again, saying officers had not arrived. At 11:35 p.m., the dispatcher told her police were on the way.
Officers Matthew Harrity and Mohamed Noor arrived on the scene a short time later.
As they drove down the alley in their police car, Harrity heard a loud sound that startled him, the officer told state investigators.
That's when Ruszczyk approached Harrity's driver's side window. Noor, sitting in the passenger seat, fired his gun and shot Ruszczyk through the driver's side window, Harrity told the Minnesota Bureau of Criminal Apprehension, or BCA, which is leading the investigation.
Audio: Officers scrambled to save woman's life
Immediately after Ruszczyk was shot, both officers got out of the car and tried to help save her, Harrity told investigators.
Dispatch audio from the officers captured the anxiety as they waited for an ambulance to arrive.
"(Squad) 530, uh, shots fired," one of the officers says. "Can we get EMS code 3, Washburn and 51st Street? We've got one down."
The dispatcher then calls for other units, and an officer -- it's not clear which -- says someone is starting CPR.
An officer tells other units they are in the entrance of an alleyway between houses.
The dispatcher asks the officer on the radio whether the situation is under control, and whether the ambulance can safely approach the shooting scene.
The officer says it's safe. "There are no suspects at large," he says.
Later, an officer's voice gets increasingly tense while waiting for the ambulance.
"Where is EMS on this?" he says.
The audio was provided to CNN by the operator of Minnesota PoliceClips, a company that monitors and records police radio dispatches.
Neither police nor the city of Minneapolis communications department would verify the authenticity of the Minnesota PoliceClips recording. But Assistant Police Chief Medaria Arradondo confirmed that, after canvassing the area, the officers found no evidence of sexual assault.
For days, Ruszczyk's family and the mayor of Minneapolis have expressed growing frustration about the slow trickle of information from the Bureau of Criminal Apprehension.
Noor has invoked his right not to speak to investigators, the BCA said Tuesday, something which Mayor Betsy Hodges has urged him to do.
"He has a story to tell that no one else can tell," she said. "We can't compel him by law, but I wish that he would make that statement."
The case is also hampered by a lack of video footage. The squad car's dashcam was not turned on and neither of the officers' body cameras were on at the time, officials said. The department says it will review its body camera policy.
Minneapolis police policy says body cameras should be turned on prior to use of force "as soon as it is safe to do so" and during "any contact involving criminal activity."
Investigators also want to talk to a man on a bicycle who watched police perform CPR on Ruszczyk, and are asking him to come forward.
It could take two to four months before the BCA finishes its investigation, said Chuck Laszewski, a spokesman for the Hennepin County attorney's office.
Once that happens, Hennepin County attorney Mike Freeman -- not a grand jury -- will decide whether either of the two officers involved should be charged in Ruszczyk's death.