"She came out bleeding, screaming, came in front of our house and ask for help. She called the police," said one neighbor.
After a two-hour standoff, the SWAT team stormed into the suspect's home and fatally shot him.
The suspect was identified by family members as 32-year-old Geraldo Arvallo.
"They could have gave us, the family, the opportunity to at least talk to him, to let us, give me one minute, and I know I could have brought him, and I know my brother would still be alive right now," said the suspect's sister Lucy Arvallo through her tears.
The toddler is safe, but her mother, 29-year-old Laura Sibrian, is in the hospital, and her father is dead.
"He refused to surrender or release his daughter, while making threats to kill himself," Deputy Ed Ward said.
Deputies said they believed the child was in imminent danger and fired a single shot that killed Arvallo when he was not near the child.
"The emphasis for us was the safety of the child and getting her to safety, and that was unsuccessful. He refused to release her, and that's why it ended the way it did," said Capt. James Hellmold from the L.A. County Sheriff's Department.
Relatives of the suspect said the couple had problems, but they're still convinced that police did not have to kill him because they say he would not have done anything to harm his child.
"I know my brother, he loves his daughter. I know he didn't have her hostage," said the suspect's brother Eloy Arvallo. "My brother knew that he was gonna go to jail. He just wanted to spend a little time with his daughter 'cuz today was her birthday. It was her birthday today."
His brother said Arvallo had a police record and was scheduled to go to jail because of other issues.
The Sibrian is in stable condition at the hospital.
The Associated Press contributed to this story.
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