But the suspect they arrested late last week didn't fit their expectations.
Police say Sandra's killer is 28-year-old Melissa Huckaby, a Sunday school teacher and the mother of one of Sandra's close friends. Huckaby allegedly killed the second-grader and dumped the suitcase containing her body in a nearby irrigation pond.
Though little is known about Huckaby or a possible motive, if the allegations are true, Huckaby would not fit the typical profile of a killer. According to the Justice Department, roughly one in 10 homicides are committed by women. And when women kill, their victims are more likely to be someone close to them, like their children, boyfriends or spouses.
Forensic psychologists and criminal profilers say women who kill have backgrounds and motivations that are often quite different from their male counterparts. Compared with men, women are more likely to be related to their victim, less likely to plan in advance and less likely to use extreme violence.
"Women are different in whom, how and why they kill," said James Alan Fox, a criminologist at Northeastern University. "The victims are younger, they're more often related to them, they kill with means other than guns.
"The traditional female role is a nurturer, not a murderer. Extreme violence is far more alien to females than to males," he added. "When a murder is committed by a female, it's more likely to be self-defense or can reflect some sort of mental illness."
Though women committed roughly 10 percent of murders between 1976 and 2005, they were involved in nearly 35 percent of murders of intimate partners and nearly 30 percent of murders of where the victim was another family member, according to the Justice Department.
So far, police have not released a possible motive for Cantu's death. Prosecutors told the Associated Press Monday that they are considering rape and molestation allegations against Huckaby. San Joaquin County Deputy District Attorney Robert Himmelblau told The AP Monday that a homicide charge against Huckaby could also include the special circumstances of rape with a foreign object, lewd and lascivious conduct with a child and murder in the course of a kidnapping.
Sgt. Tony Sheneman declined comment on whether or not Huckaby may have shared any details about how Sandra died. He said autopsy results would yield further information when they are released, likely in several weeks.
Family members said Huckaby, the granddaughter of the local pastor, was a devoted mother to her 5-year-old daughter.
"We're very, very shocked," said Joani Hughes, Huckaby's aunt. "It's very out of character for Melissa."
But her father, Brian Lawless, said that his daughter had often struggled with raising a child on her own and had sometimes suffered from bouts of depression.
"I have no doubt in mind she knows right from wrong," her grandfather, Clove Road Baptist Church pastor Lane Lawless, said. "At least I thought she did. Maybe I'm mistaken."
Brian Lawless said he's visited his daughter in jail and that they cried together.