State authorities in Minnesota have completed their investigation into the fatal police shooting of Australian woman Justine Damond and have turned the case over to the county attorney to decide whether charges will be laid.

Officer Mohamed Noor has been on paid leave since the shooting. ( Star Tribune: City of Minneapolis )

Damond's fiance, Don Damond, released a short statement saying, "The wait continues for Justine's family and me".

"We want to see justice for Justine and hope that the Hennepin County Attorney will act swiftly to review the findings and determine charges," he said.

Damond was shot and killed by officer Mohamed Noor in Minneapolis on July 15, after calling police about a possible sexual assault near her house.

The shooting sparked outrage in Minnesota and Australia and triggered the resignation of the Minneapolis police chief.

Damond family attorney Bob Bennett said the family believed the officer should be held accountable.

"They certainly believe charges are merited," he said in a telephone interview with Reuters.

Hennepin County Attorney Mike Freeman will now review the case to determine what charges might be brought.

Officer Noor has been on paid leave since the shooting.

On Sunday, Mr Freeman told a community forum Justine's death, "shouldn't have happened".

The Bureau of Criminal Apprehension said it would continue to work with the county attorney to provide further information as needed.

A decision is expected by the end of the year.