Updated

Police in Orlando, Fla., are interviewing dozens of acquaintances of Casey Marie Anthony whose two-year-old daughter, Caylee, has been missing for more than a month.

"We believe Casey knows where the girl is because everything she’s told us so far has turned out to be lies," Orlando sheriff's spokesman Carlos Padilla told FOXNews.com on Sunday.

"We're making phone calls to anyone who has had contact with her to see if she's said something," Padilla said.

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On Saturday, the mother's attorney suggested his client's toddler daughter, Caylee might have been taken out of state — possibly to Miami; Charlotte, N.C.; or even New York City, according to MyFOXOrlando.com.

Baez did not explain why he believes the child might be outside the area where she lived. He said the investigation into Caylee's disappearance has been hindered by her 22-year-old mother's imprisonment.

"I think her detention is actually hampering the search," Baez told MyFOXOrlando.com. "It's just counterproductive."

Orange County detectives spent Friday digging through the backyard of Caylee's grandparents, Cindy and George Anthony, in hopes of turning up clues in the child's disappearance.

Cadaver dogs were at the scene, and several items were removed from the Orlando home, which became the focus of the investigation after a neighbor said Casey Anthony had borrowed a shovel about a month ago. Police found and took the shovel as evidence.

"This is difficult, tedious work," sheriff's Sgt. John Allen, who oversees the department's child abuse and missing persons division, told reporters during a press briefing Friday. "Just because we’re here with cadaver dogs doesn’t mean we’re giving up hope that Caylee is alive."

Allen said they have not found signs of the girl in the yard but it is only "one of several places we're looking." He would not elaborate.

Casey Anthony has been in custody since Wednesday, when she finally told authorities the child was missing. A day earlier, Caylee's grandparents filed a report after learning their daughter's car had been towed from a location that was nowhere near where she claimed to be staying.

The little girl lived in the house with her mother and grandparents until June 9, when Casey said she vanished.

"When all of the facts come out, it will be a little bit more understandable as to why there was a delay in time in this case," Baez told MyFOXOrlando.com.

Caylee's grandparents had been "very cooperative" in the investigation, according to Allen; the sheriff's office said the search of their property in no way implicated them in the case.

"It's very clear to us that they want their granddaughter back," Allen said.

Cindy Anthony said she wants the focus for now to be on finding little Caylee, not on her daughter's arrest.

"I will look in every nook and cranny until I find her," she told MyFOXOrlando.com, breaking down in tears. "I know in my heart that she's alive."

The hunt for evidence began Thursday night but stopped when darkness fell, resuming Friday morning. Detectives found "abnormalities" in the dirt that caused them to be suspicious, according to MyFOXOrlando.com. They searched for much of the day, suspending their efforts in the afternoon.

Described by friends as a "habitual" and "compulsive" liar, Casey Anthony told investigators that she dropped Caylee off with a friend on June 9. Authorities have been unable to locate that woman or verify anything else Anthony told them.

The FBI told FOXNews.com that the bureau is aware of the case but is not playing a part in the probe.

"We're definitely aware of it and monitoring the situation, but that's the extent of our involvement," said Special Agent Dave Couvertier, a spokesman for the Orlando and Tampa FBI.

Orange County Sheriff's Capt. Angelo Nieves said the grandparents' property on Hopespring Drive is central to the investigation, according to the Orlando Sentinel. Allen said sheriffs spent several hours with Casey Anthony after her arrest, but procedural regulations have barred them from interviewing her further in jail without her attorney.

Neighbor Diana Centeno, whose children have played with Caylee in the past, called the situation "scary," according to the Sentinel. She said she hoped Casey Anthony didn't have anything to do with the toddler's disappearance.

Anthony was arrested Wednesday on charges of child neglect and providing false information to law enforcement. She showed no emotion Thursday as she was ordered held without bond at the Orange County Jail.

The judge scolded the mother, saying she had "no regret or concern for her actions," the Sentinel reported.

"You left your 2-year-old child with a person who does not exist at an apartment you cannot identify and you lied to your parents about your child's whereabouts," Judge John Jordan said. "You cared so little about your child."

He ordered a mental health evaluation be done on Anthony, according to the newspaper.

The Orange County Sheriff's Department told FOXNews.com that they have no reason to believe the toddler is dead.

"[We are] still operating under the hope she is going to turn up alive," Deputy Sheriff Carlos Padilla said Thursday.

Padilla said Anthony claims the child's father is dead — something authorities are still looking into.

Investigators said their job has been made more difficult because Anthony continues to spin stories that aren't true.

"Based on the repetitive lies that the defendant has told, we do not know with whom the child is or even if the child is alive," sheriff's Cpl. Yuri Melich wrote in the arrest affidavit, according to the Sentinel. "It should be noted that at no time during any of the above interviews did the defendant show any obvious emotion as to the loss of her child."

Anthony told her mother that she was being sent to Tampa for work and would be back in a few days, but later changed her story and said she was going on a "mini-vacation," according to the Sentinel.

"I had no reason to believe they weren't where they were supposed to be," Cindy Anthony told the newspaper. "I don't know why she fabricated this."

It was not clear why Casey Anthony didn't report her daughter missing earlier.

"I’ve had the feeling the past couple of weeks that Casey's been holding back," Cindy Anthony told MyFOXOrlando.com. "I’ve been asking to speak with my granddaughter and she’s been making excuses that I can't talk to her because she’s with someone else or she’s swimming or napping."

Casey Anthony told police that her daughter wasn't at the baby sitter's house when she went to pick the child up, so she started to do her own investigation.

She went to clubs that the baby sitter frequented and identified her as Zenaida Gonzalez, police said. But when detectives went to the apartment Anthony said belonged to the alleged baby sitter, they learned it had been vacant for almost five months, the newspaper reported.

Once detectives caught up with Gonzalez and showed her pictures of both Anthony and Caylee, Gonzalez said she didn't recognize them.

George Anthony said his daughter wouldn't hurt Caylee.

"My daughter is a fantastic mother," he told FOX News. "She was nurturing, she always did the right thing. ... I never once saw my daughter raise her voice."

Allen said police want to keep the case in the public eye, and are following up on numerous leads that have come in because of the media coverage.

The Orange County Sheriff's Office is asking anyone who has seen Caylee to call the crime line at 1-800-423-TIPS.

Click here for more of the interview with Casey Anthony's lawyer from MyFOXOrlando.com.

Click here for more on the search for clues from MyFOXOrlando.com.

Click here to read more on this story from the Orlando Sentinel.

FOX News' Catherine Donaldson-Evans, Michelle Maskaly and The Associated Press contributed to this report.