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Prosecutors and a defense attorney for a Florida mother charged in the death of her 2-year-old daughter each presented new, vastly different theories of how the little girl died as the trial for Casey Anthony began Tuesday.

For the first time, prosecutors said Caylee Anthony died from three pieces of duct tape being placed over her mouth and nose while a defense attorney for the mother claimed the toddler drowned in the family pool and the little girl's grandfather helped cover up the accident.

Casey Anthony, 25, is charged with first-degree murder. If convicted, she could be sentenced to death.

An autopsy was never able to conclude a cause of death for Caylee.

Casey Anthony waited a month before telling her mother that Caylee had disappeared during the summer of 2008, and that was only after her parents, George and Cindy Anthony, had recovered a car Casey had been driving, prosecutors said. The vehicle, which the grandparents picked up from a towing lot, had a foul odor inside.

During the month Caylee was missing, prosecutor Linda Drane Burdick told jurors Casey went shopping, visited friends and hung out with her boyfriend. Between each description of how Casey spent her time, Burdick said: "Where is Caylee Marie Anthony?"

She also described Internet searches done on a computer at Casey's home that showed queries for chloroform, neck-breaking and alcohol.

Prosecutors said everything Casey Anthony did was based on a web of lies and that the evidence points to her as the killer.

"Casey Anthony ... appeared to be ... a loving mother, trying to provide support for her daughter," Burdick said. "But as the evidence in this case will show, that was an illusion."

Casey previously said a baby sitter kidnapped the girl, but her attorney suggested a different set of events during his opening statement.

Casey's attorney, Jose Baez, said she was molested by her father as a child, an allegation George Anthony denied on the witness stand. George Anthony also told jurors that Caylee didn't die at his house, and he denied disposing of her body and placing duct tape over her face.

"I would have done everything possible to save my granddaughter if what was said happened, happened," said George Anthony, the only witness to testify so far.

Baez also claimed that Casey's brother made advances toward her and was given a paternity test to see if he was Caylee's father. All those secrets eventually led to the cover up of Caylee's drowning, Baez said.

"You will hear about a family that is dysfunctional," Baez said. "Ugly things. Secret things."

Baez said Caylee and her grandmother swam most of Father's Day on June 15, 2008, and suggested that Cindy Anthony forgot to pull up a ladder that prevented the toddler from climbing into the pool on her own. Baez suggested that Caylee slipped into the pool the next day when no one was looking.

The distraught family panicked and didn't call police, he said.

"Casey should have called 911. That's what she's guilty of, she's not guilty of murder. This is not a murder case," Baez said.

Prosecutors offered a timeline of Casey's whereabouts based on cell phone records. It stretched from the time Caylee was last seen by her grandparents until Casey Anthony told her mother in mid-July 2008 that Caylee had been missing for a month.

Jurors were shown images on a screen of a photo of Caylee taken on Father's Day alongside an image of the little girl's skeletal remains.

During a lengthy opening statement, Baez said George Anthony planted duct tape matching the brand later found over Caylee's mouth in a way that would implicate Casey.

"George Anthony took certain steps to make sure he was as far away from this situation and that Casey would end up taking the blame for this," Baez said.

A meter reader discovered Caylee's remains, some as small as a pebble, in a wooded area in December 2008 about a half-mile from where the child lived. Her skull was covered with duct tape that had residue from a heart-shaped sticker on it.

Baez questioned whether the meter reader, Roy Kronk, actually found Caylee's bones where he said he did or whether he moved them from another location. Baez didn't explain where Kronk may have initially discovered the remains.

Baez also blamed the police department for botching the investigation, alleging detectives wanted to feed a media frenzy about a mother killing her child instead of investigating a mundane drowning.

Police "had murder on their minds. This couldn't be an accident," Baez said. "You'll find that professional police work took a backseat in this case. We were more concerned about the public than doing their jobs."

Casey was emotional throughout the day, crying periodically and wiping her nose with a tissue.