Officers found the dead boys ages 2 months old and 5 and 8 years old in a closet full of miscellaneous items. The youngest boy's body was in a case of some kind in the closet, Sgt Trent Crump said yesterday.
No identities were released.
"Detectives have informed me that it appears the children at this point were likely stabbed to death and parts of their bodies were dismembered," Crump said.
The woman's brother called 911 early yesterday after his sister stabbed herself some time after he returned from work to their northwest Phoenix home late Wednesday, police said.
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The woman initially spoke with her brother in the garage but then locked him out of the house and then locked herself in a bedroom once he forced his way into the home, Crump said.
She then came out all bloody, having stabbed herself, and she tried to drown herself in a bathtub while the brother was getting towels for her bleeding, the sergeant said.
As she was being taken to the hospital, the woman told police her sons were staying with a baby sitter, and the brother told police the boys did regularly stay with that person, Crump said.
The mother was hospitalised in critical condition with neck and abdomen wounds but is expected to survive, police said.
"She will be in the hospital for some time with some very serious self-inflicted injuries," Crump said. "It's a murder investigation at this point."
The brother told police he didn't understand why his sister recently had started talking about religion, and family members "don't know what set this off," Crump said, referring to the killings.
The woman and her children live with her brother and the siblings' mother, Crump said. "There's no father in the picture.