But Stanislaus County District Attorney Jim Brazelton says he wouldn't call this or any murder case a "slam dunk."
Indeed, Scott Peterson — who pleaded not guilty Monday to the charges against him — might claim that police devoted too much attention to him and not enough to any other suspects, CBS News Legal Analyst Andrew Cohen notes.
"If the defense can give some examples of this, the case may be a closer call than most people think," Cohen reports.
In another challenge for prosecutors, Brazelton says it will be difficult to determine exactly how Laci Peterson died because her body was badly decomposed. Documents filed Monday by prosecutors said the killings happened at the Petersons' Modesto home on Dec. 23 or Dec. 24.
The bodies of Laci Peterson and her unborn baby boy washed ashore last week about three miles from where Scott Peterson said he was fishing in San Francisco Bay when his wife vanished.
Peterson entered his plea Monday during a brief arraignment in Stanislaus County Superior Court in Modesto. Brazelton said in his filing that Peterson, 30, acted "intentionally, deliberately and with premeditation" in killing 27-year-old Laci Peterson and Conner Peterson, the couple's unborn child.
California law permits a murder charge for a fetus if a pregnant woman is slain, even if the fetus is not viable, said Hallye Jordan, spokeswoman for the state attorney general.
The charges against Peterson include the special circumstance that he allegedly committed multiple homicides, which would let prosecutors seek the death penalty. Brazelton said his office would probably decide by a May 19 hearing whether to seek the death penalty.
Public defender Tim Bazar was assigned to the case after Peterson said he could not afford to hire a lawyer. The case was continued until a May 6 bail hearing.
Investigators had long declined to name Peterson as a suspect, but even before DNA tests identified the bodies, Modesto police arrested him Friday near San Diego because they feared he might flee to Mexico, according to Modesto Police Chief Roy Wasden.
Brazelton told the CBS News Early Show that during the probe, Scott Peterson's demeanor was "different than any I've ever seen in many years in this business."
"A lot of the things that he did or was reported to have done did not appear to be consistent with someone who had just lost their wife and soon-to-be son," Brazelton said.
Brazelton contends the publicity surrounding the case would not taint the jury pool. "I feel that we can select a fair and impartial jury in this county. You'd be surprised how many people don't read the paper, don't watch television news," he said.
When he was arrested, Peterson's naturally dark hair was reddish-blond, he had grown a goatee. He had $10,000 in cash with him in his car, said a law enforcement source who spoke on condition of anonymity.
Defense lawyer Kirk McAllister, who had represented Peterson before the arraignment and met with him in jail Saturday night, said there was a good explanation for the cash his client had during his arrest, but declined to discuss that or other elements of the case.
In a press conference held Monday evening, Laci Peterson's family said they would not jeopardize court proceedings by commenting on Scott Peterson's possible involvement in her disappearance, then thanked those who helped search for their missing daughter.
In an emotional statement, Laci Peterson's mother, Sharon Rocha said the person responsible for Laci's death "should be held accountable and punished for the tragedy and devastation forced upon so many of us."
"I can only hope that the sound of Laci's voice, begging for her life, begging for the life of her unborn child, is heard over and over and over again in the mind of that person every day for the rest of his life," said Rocha.