Read more about this story from CNN affiliate KGTV.
El Cajon, California (CNN) -- The body of an Iraqi woman, whose brutal beating death may have been a hate crime, will be flown home for burial.
Shaima Alawadi, a 32-year-old mother of five, died of a severe head injury after the attack at her home in southern California March 21. A note beside the body told the family to go back to Iraq and called them "terrorists," her daughter said.
Alawadi, who was hospitalized in critical condition after the beating, was taken off life support Saturday.
A memorial service will be held Tuesday at her home, organized by the local Muslim community.
The U.S. State Department Tuesday expressed its condolences to Alawadi's family.
State Department spokeswoman Victoria Nuland called the attack an "absolutely brutal beating," and said "authorities are continuing to search for motives behind this attack, but the United States has no tolerance for wanton acts of violence like this."
Late Monday night, the Council on American-Islamic Relations (CAIR) said Alawadi's body would be taken to Iraq for a funeral and burial.
Hanif Mohebi, executive director of the organization that advocates for Muslim civil liberties, said he did not know exactly when the funeral will take place, but believed the Iraqi government was footing the bill to transport the body.
A spokesman for the U.S. Embassy in Baghdad said the Iraqi government had not requested help in repatriating Alawadi to Iraq, but were willing to assist if asked.
Alawadi and her husband have three daughters and two sons, ranging in age from 8 to 17, Mohebi said. They moved to the San Diego County area in 1995 and then briefly lived in Dearborn, Michigan, before moving back to California.
Both El Cajon, where the family lived, and Dearborn have sizable Iraqi communities -- among the nation's largest.
Alwadai's teenage daughter found her mother unconscious in the dining area of their home last week.
The note lay beside her body, Fatima Al Himidi told CNN affiliate KGTV. Nothing was stolen from the house.
Police have not disclosed the contents of the note, but called it "threatening."
"Based on the content of the note, we are not ruling out the possibility that this may be a hate crime," city Police Chief Jim Redman said Monday.
"Other evidence," however, leads investigators to remain 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.
Al Himidi told KGTV that a similar note was left outside the family home earlier in the month, but the family did not report it. Police confirmed it.
"A week ago they left a letter saying, 'This is our country, not yours, you terrorists,'" she said over the weekend. "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."
Mohebi said the family was holding up as best as they could, amid an outpouring of support from the community.
"But they're also emotionally realizing that yes, their mother is no longer with them. And that's heartbreaking," he said.
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.
CNN's Alan Duke, Samira Said, Maria P. White and Chuck Conder contributed to this report.