Casey Anthony's lawyers filed the motions a day after the State Attorney's Office released hundreds of pages of documents related to the case.
Anthony's attorneys said prosecutors can't prove first-degree murder was committed or that Anthony ever abused her daughter, Caylee.
"Specifically, the state cannot establish whether Caylee Anthony's death was accidental, natural, or the result of an intentional or negligent homicide," they said.
On "The Early Show" Friday, Todd Macaluso, a lawyer for Casey, said bluntly, "Casey Anthony is innocent, she will be proven innocent. The state has not produced any evidence whatsoever to prove their case. The case should be dismissed."
The 23-year-old woman has pleaded not guilty and claimed that a baby sitter kidnapped Caylee.
The toddler's remains were found last December, five months after she was reported missing, in woods near the home where she lived with her mother and grandparents. Although the death was ruled a homicide, a specific cause was never determined.
Meanwhile, an attorney for Anthony's parents released an FBI forensics report that he said shows duct tape found with Caylee's remains doesn't match duct tape found at the Anthony home, key evidence in the state's case.
The forensics report released by attorney Brad Conway appeared to contradict an earlier report that had determined the tape on the skull and that found on gas cans at the Anthonys' house originated from the same roll of tape.
Also in focus -- DNA found on the tape that doesn't match any member of the Anthony family, but is a match for an FBI lab technician who handled it.
"If there's an FBI analyst's DNA on a piece of tape that's a critical piece of evidence, that's bad news for the prosecution," says CBS News legal analyst Lisa Bloom.
Forensic tests on Casey's car revealed the presence of chloroform, and evidence of human decomposition. But an internal FBI e-mail cited by Casey's lawyers says hair found in the car that's microscopically similar to Caylee's isn't from her.
The defense argues much of the case is circumstantial, and there's a lack of physical evidence implicating Casey in her daughter's murder.
On "The Early Show", co-anchor Maggie Rodriguez asked Macaluso and fellow Casey Anthony defense attorney Jose Baez how they will "explain the fact that Casey did not report her daughter missing for a month, that she was out partying when Caylee was supposedly missing, and that she lied to investigators trying to help her find Caylee?"
Baez responded, "We feel that Casey has a very compelling reason for her actions, and we plan on laying them out at trial. That's the proper place for us to lay out a defense."