It's been four days since 35-year-old Ajike "AJ" Owens was shot and killed in central Florida after knocking on a neighbor's door.

Owens' family want the person who killed her arrested and charged.

They say the shooter, identified by police reports only as a 58-year-old White woman, harassed the Black mother and her children and had called them racial slurs prior to the killing.

Marion County Sheriff Billy Woods told reporters Monday his office is rigorously investigating the case, but referenced the state's "stand your ground" law as a reason why authorities have not arrested the shooter.

Authorities are working to determine "whether the deadly force was justified or not," Woods said.

Fifth Judicial Circuit Chief Assistant State Attorney Walter Forgie told CNN Tuesday the office is working with the sheriff's department in the investigation and a "prompt charging decision" will be made "once all of the evidence has been collected and analyzed."

Here's what we know.

How the shooting unfolded

The sheriff gave a brief description of how the Friday shooting unfolded during his Monday news conference, but stressed that authorities had largely heard only the shooter's side of the story and were still working to interview children, who were key witnesses to the shooting.

The shooter has been cooperating with authorities, Woods said.

Deputies responded to a trespassing call after 9 p.m. Friday night and found Owens laying in the grass, suffering from a gunshot wound, according to an incident report from the sheriff's office. She was later pronounced dead at a hospital, authorities have said.

The shooter had earlier "engaged" with Owens' children and threw a pair of skates, hitting them, Woods said.

One witness told police there had been a dispute over a child's electronic tablet device before the shooter threw the skates, according to the incident report.

A child then went back inside their home and told their mother -- Owens -- about the incident, who went to the neighbor's home to "confront" her, Woods said.

The shooter told police there had been "a lot of aggressiveness" from both sides before she shot Owens through the door, according to the sheriff.

Witnesses told authorities Owens went to the shooter's home and knocked on the door before she was shot, according to the incident report.

The neighbor's door "never opened" when Owens tried to confront her, according to Pamela Dias, the victim's mother.

"My daughter, my grandchildren's mother, was shot and killed with her 9-year-old son standing next to her. She had no weapon, she posed no imminent threat to anyone," Dias said in a separate news conference held by the family's attorneys Monday.

Sheriff mentioned "stand your ground" law

Florida's "stand your ground" law allows people to meet force with force if they believe they or someone else is in danger of being seriously harmed by an assailant.

Under the law, a person can use deadly force anywhere as long as he is not engaged in an unlawful activity, is being attacked in a place he has a right to be and reasonably believes that his life and safety are in danger as a result of an overt act or perceived threat committed by someone else, CNN has previously reported.

"That law has specific instructions for us in law enforcement," the sheriff said. "Any time that we think, or perceive or believe that that might come into play, we cannot make an arrest, the law specifically says that."

"What we have to rule out is whether the deadly force was justified or not before we can even make the arrest," he said, adding: "I wish our shooter would have called us instead of taking actions into her own hands."

Though the sheriff did not explicitly say why he referred to that law, the mention of it ignited backlash from Owens' family and their attorneys, who say there is no way to justify Owens' killing.

In a verified GoFundMe page, Owens' family said "stand your ground" laws have "emboldened individuals to use unnecessary violent force in the name of self-defense," and said they have partnered with national advocacy groups to promote change.

"(The shooter) could have called 911. She could have did 100 other things ... than to use deadly force," civil rights attorney Ben Crump, one of the attorneys representing the family, told MSNBC on Monday. "It is unacceptable."

A single mom who 'loved her children unconditionally'

Owens was described by family as a single mother of four who was full of life, loved her children "with all her being" and helped those around her in any way she could.

She was described on the family's GoFundMe as a devoted mother and Christian whose smile would light up a room and who would do anything for those she loved, both family and friends.

"To say she loved her children unconditionally is an understatement. She was a single mother whose life centered around her children. She was the Team Mom for her children's football/cheerleading teams," according to the page.

"She often would give to other single mothers that were in similar situations that she'd been in," it added.

The page also said Owens "excelled professionally as a manager" in the restaurant and hospitality industry.

"Honestly, I don't even know how she did it. She is an amazing testament to all mothers in this world," Dias told MSNBC.

The GoFundMe for Owens' family had raised more than $85,000 as of Tuesday evening.