Story highlights Police chief: "Other evidence" leads investigators to keep open to possibilities

Police "strongly believe that this was an isolated incident," the chief says

A note "threatening in nature" was found near the beaten woman, police say

Shaima Alawadi had been on life support since the attack Wednesday

The possibility that the killing of an Iraqi woman who was left brutally beaten in her Southern California home last week was a hate crime is "just one aspect" being investigated, a police official said Monday.

Shaima Alawadi, a 32-year-old mother of five, died of a severe head injury after she was taken off life support Saturday, El Cajon, California, Police Chief Jim Redman said at a news conference.

A note that was "threatening in nature" was found near where her 17-year-old daughter discovered her lying unconscious in the dining area of her home in El Cajon in San Diego County last Wednesday, Redman said.

Redman would not specify what the note said; the daughter said it told the family to go back to Iraq and called them "terrorists."

"Based on the content of the note, we are not ruling out the possibility that this may be a hate crime," Redman said.

"Other evidence," however, leads investigators to keep open to other possibilities, he said. "The possibility that this is a hate crime is just one aspect of what we are examining."

Although the investigation is "still in the early stages" and police "have not drawn any conclusions," Redman did say evidence leads them to "strongly believe that this was an isolated incident." The chief would not describe that evidence.

Detectives obtained a search warrant for the family's home because a court order is "just the best way to recover evidence," Redman said.

The daughter, Fatima Al Himidi, told CNN affiliate KGTV that a similar note was left outside the family home earlier in the month, but the family did not report it.

"A week ago they left a letter saying, 'This is our country, not yours, you terrorists,'" she said. "So my mom ignored that, thinking (it was) kids playing around, pranking. And so the day they hurt her, they left it again and it said the same thing."

Hanif Mohebi, executive director of the San Diego chapter of the Council on American-Islamic Relations, said the family came to the United States from Iraq in the mid-1990s. He did not know when they moved to El Cajon, which has one of the nation's largest Iraqi communities.

Alawadi and her husband have three daughters and two sons, ranging in age from 8 to 17, Mohebi said.

Fatima Al Himidi said nothing was stolen from the house, leading her to believe the attack on her mother was motivated by hate.

"Why did you take my mother away from me? You took my best friend away from me," she said, choking with tears, in an interview with CNN affiliate KUSI. "Why? Why did you do it? I want to know. Answer me that."

Social media users quickly compared Alawadi's death to that of 17-year-old Trayvon Martin, calling both hate crimes, and drawing a parallel between a hijab and a hoodie.

Martin was killed last month as he walked back to the house of his father's fiancee in Sanford, Florida, after a trip to the convenience store. Police say he was shot by George Zimmerman, a neighborhood watch volunteer who said he was acting in self-defense and has not been charged.

The teen was unarmed, carrying a bag of Skittles candy and an iced tea, and was wearing a hoodie.

On Sunday morning, the authors of the parenting blog Momstrology tweeted: "A teen murdered for wearing hooded sweater. An Iraqi woman beaten to death for wearing a head scarf. Our hearts ache for you."