By Brad Parks, Emanuella Grinberg and Holly Yan

CNN

MINNEAPOLIS (CNN) -- Justine Ruszczyk's relatives say they're still stunned the bride-to-be was killed by police -- and they've hired an attorney with experience handling controversial police-involved shootings.

"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 released to CNN affiliate Sky News Australia.

"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."

Ruszczyk, 40, was originally from Australia but moved to the United States in 2014. She was set to marry her fiancé, Don Damond, next month.

But on Saturday night, Ruszczyk was killed minutes after calling 911 to report a possible sexual assault.

The Ruszczyk family's attorney is calling for a comprehensive investigation and policy review.

"The family is interested in justice in (the) largest sense -- an unbiased, transparent investigation, necessary changes in police training, officer selection criteria and practice, proper and non-discretionary policies on usage of forensic tools, including squad and body cameras, swift and sure discipline and full and complete recompense," Robert Bennett told CNN in an email Thursday.

Bennett has experience representing families in police-involved shootings in the Minneapolis area. He was one of the attorneys for the family of Philando Castile, who was killed by St. Anthony police Officer Jeronimo Yanez last year.

Castile's death garnered international attention after his girlfriend broadcast the shooting's aftermath on Facebook Live. While the police officer was acquitted of manslaughter, the city of St. Anthony reached a $3 million settlement with the Castile family.

Ruszczyk's death has also attracted wide coverage, and her family and friends have been demanding answers, but it could be months before Minnesota authorities finish their investigation.

911 calls lead to police encounter

Some of the first clues emerged this week about what may have led to the police shooting of Ruszczyk.

She made two 911 calls Saturday night to report a possible sexual assault near her home, according to transcripts the city released 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 the Minnesota Bureau of Criminal Apprehension.

That's when Ruszczyk approached Harrity's driver's side window, Harrity told investigators. Noor, sitting in the passenger seat, fired his gun and shot Ruszczyk through the driver's side window, Harrity said.

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 recording.

Answers slow

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.

But Minneapolis Mayor Betsy Hodges has urged Noor to issue a statement.

"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 was on at the time, officials said.

The department said it will review its body camera policy.

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.

CNN's Brad Parks and Ryan Young reported from Minneapolis, while Holly Yan, Carma Hassan and Emanuella Grinberg reported and wrote from Atlanta. CNN's Joshua Berlinger, Dave Alsup and Euan McKirdy contributed to this report.