"Nothing is more heartbreaking than the tragic betrayal of a parent failing to protect their children."
The children were found dead in a bedroom of their home on Monday.
Authorities have said there were no obvious signs of trauma and authorities hadn't been called to the home by any previous indications of trouble.
The prosecution statement didn't specify the cause of death. However, family members have said Chico suffered from depression and that she suffocated them and then tried to kill herself, KABC-TV reported.Chico was initially detained, and authorities announced her arrest on Tuesday.
The coroner's office identified the children as Mia Camila Rodriguez, 4, and her brothers Mason Mateo Rodriguez, 3, and Milan Mateas Rodriguez, who was 1 month old.