Sandra disappeared on March 27 and hundreds of volunteers and law enforcement officials turned out to search for her. On April 6, farmworkers draining an irrigation pond found the suitcase.
Huckaby walked into the police station Friday and started a conversation with officers, Sheneman said at a news conference.
"She was calm, cool and collected, then she became very emotional .... She went back and forth from being calm to emotional."
Eventually, she became "resigned," Sheneman said.
"I couldn't begin to even theorize what her motive was," he said.
"Sandra was very close friends with Melissa's daughter. They used to play together," Sheneman said.
Investigators know where the girl was killed but can't disclose the location, he said. Autopsy results are not yet available. He wouldn't say whether police believe the slaying was accidental or deliberate.
Sheneman had earlier told The Associated Press that interviews with Huckaby in The Tracy Press had revealed inconsistencies that prompted further inquiries from investigators.
He had confirmed early Saturday that the suitcase in which the body was found belonged to Huckaby.
Huckaby is on suicide watch in an observation cell, said sheriff's Deputy Les Garcia. She is refusing to see visitors, he said. Jail records did not indicate whether she had an attorney. Sandra's aunt, Angie Chavez, said the girl's mother, Maria Chavez, was devastated.
"It's not over. This is just the beginning of a horrible nightmare," Angie Chavez said of the arrest as she stood at the entrance to the mobile home park where Sandra lived with her mother.
Angie Chavez' husband, Joe Chavez, said Huckaby should face the death penalty.
"You eye everybody with a great deal of suspicion. We're shell-shocked here," Joe Chavez said. "Who can you trust at this point? Who do you know?"
Susan Levy of nearby Modesto, mother of slain Washington intern Chandra Levy, appeared arm-in-arm with Angie and Joe Chavez as they spoke with reporters.
Levy said she was there to support the family as they, too, dealt with the tragic loss of a child. Authorities recently issued an arrest warrant in the 2001 Levy killing.
Sheneman said investigators hadn't expected that the suspect would turn out to be a woman.
"It's unusual for it to be a woman statistically and according to the FBI," he said at the news conference.
Discovering it was a woman and a member of the tight knit Tracy community who knew the family was "a double blow," he said. "Today's going to be a very difficult day for everyone to digest that," Sheneman said. "This was an anomaly in the murder of a child."
Sheneman said no other arrests in the case are anticipated. Neighbor Barbara Sokoloski, whose home is behind Sandra's, described Sandra on Saturday as "a friendly sweet little girl who always went around trying to find somebody to play with."
"It's too bad that kids these days can't go out and play like we did when I was a little girl," said Sokoloski, 69.
Huckaby had told The Tracy Press that Sandra visited her home on the day of her disappearance to play with her 5-year-old daughter. But Huckaby said she'd turned Sandra away because her daughter needed to pick up her toys and Sandra went to another friend's home. Huckaby also said she had left her suitcase in the driveway that day, and that it was missing.
The Tracy Press said Huckaby was released Thursday from Sutter Tracy Community Hospital, where she spent several days in intensive care for what she described as "internal bleeding."
Huckaby is a granddaughter of Pastor Clifford Lawless, whose Clover Road Baptist Church was searched by police. Huckaby taught Sunday school at the church and lived with Lawless in the Orchard Estates Mobile Home Park that also was Sandra's home.
Lawless did not immediately respond to a call seeking comment Saturday.
Huckaby was scheduled to appear in court on April 17 to check in with a county mental health program as part of a three-year probation sentence for a petty theft she pleaded no contest to. She told the newspaper on Friday that someone else by the same name was facing charges for the attempted theft in November from a Target store.
California Department of Corrections and Rehabilitation spokeswoman Terry Thornton said Huckaby has no state prison record.
Huckaby worked as a checker at a Food for Less grocery store in a strip mall just east of the mobile park for nearly four years, until she was fired sometime in 2004, said Matt Duncan, an assistant manager at the store now known as FoodMaxx.
"I wouldn't have anything bad to say about her, until now," he said. "I would've never suspected her to do something like this."
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Associated Press Writer Don Thompson in Sacramento contributed to this article.
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