Juror No. 7, an Asian woman in her 50s or 60s, apparently did her own research on the case, a source with close knowledge of the case told The Associated Press on condition of anonymity. Such research would violate the judge's order to consider only evidence presented at trial.
CBS News Correspondent John Blackstone reports the jury woes could be good news for Peterson.
"Turmoil in the jury room is often seen as a favorable sign for the defense," reports Blackstone. "At the very least, it could provide grounds for an appeal."
Judge Alfred A. Delucchi replaced the juror with an alternate on Tuesday. He then ordered the other 11 members of the panel to set aside any conclusions they had made during the first five days of deliberations and begin anew.
"You must decide all questions of fact in this case from the evidence received in this trial and not from any other resource," Delucchi reminded panelists. "The people and the defendant have the right to a verdict reached only after full participation."
"We're going to send you back. Start all over again and keep in touch," he added.
"What this means," says CBS News Legal Analyst Andrew Cohen "is that the jury has to start over from scratch with this new juror."
"That may mean we won't see a verdict for many days now or it could mean that the change in jury makeup really puts some steam into deliberations and generates a quick verdict. There is just no way to tell," says Cohen.
Peterson, 32, is charged with two counts of murder in the deaths of his wife, Laci, and the fetus she carried. Prosecutors claim Peterson killed Laci around Christmas Eve 2002, then dumped her weighted body from his boat into San Francisco Bay.
Deliberations were set to resume Wednesday.
The ousted juror, who remains under a court-imposed gag order, is the second juror to be dismissed in the case. The first, Justin Falconer, was replaced in June after he was seen talking to Laci Peterson's brother. His replacement, a man with both a law degree and medical license, is now the jury foreman.
Juror No. 7's replacement — a white woman in her 30s with nine tattoos and four sons — said during jury selection that she was willing to quit her bank job to serve on the jury. Her brother was in and out of prison for drugs, leading her mother to become a drug counselor, she said.
During the trial, the woman seemed particularly attentive to defense presentations, and responded positively to the many jokes of defense attorney Mark Geragos. She also smiled often and made a point of greeting the bailiffs each morning, but cried openly at the sight of the autopsy photos.
Alternate jurors have been present throughout the trial in the jury box but have not been inside the jury room during deliberations. They are also sequestered along with regular jurors at an area hotel.
If they ultimately conclude that Peterson killed his pregnant wife and her fetus on Christmas Eve 2002, they must decide whether he's guilty of first- or second-degree murder.
First-degree convictions, carrying the death penalty of life without parole, would mean jurors believe Peterson planned the killings. Second-degree murder convictions don't require a finding of premeditation, and carry sentences of 15-years-to-life for each count.
Judging from the ousted juror's statements during jury selection and her demeanor throughout the trial, Dean Johnson, a former San Mateo County prosecutor closely watching the case, felt she would be sympathetic to the defense. "And now she's gone after apparently doing individual research to bolster whatever opinions she had," he said.
Her replacement, on the other hand, seems so emotionally involved in the case that it might be difficult for her to separate her feelings from the facts, Johnson said. "She's not going to be able to take her emotions out of the equation here."
"This could have been a whole lot worse because the judge could have discovered that the juror who apparently went astray tainted the rest of the jury and in that scenario we would have seen much more than a change in the makeup of the jury," says Cohen. "We would have seen a quick mistrial."