(CNN) -- Investigators pleaded Monday for swift public help in reconstructing events leading to the disappearance of a 10-year-old Hickory, North Carolina, girl after casting doubt on her stepmother's story.
"We are running out of time, folks," Police Chief Tom Adkins told reporters Monday afternoon. "The longer this thing goes, the likelihood [is] that this outcome will not be positive."
Zahra Clare Baker was last seen sleeping in her bedroom about 2:30 a.m. Saturday, according to Hickory police. She was reported missing about 2 p.m. Saturday by her father, Adam Baker, and stepmother, Elisa Baker.
Adam Baker is cooperating with investigators, Adkins said. But Elisa Baker has been jailed on an outstanding warrant for a bad-check charge, prosecutors said, and Adkins said unspecified "inconsistencies" in her statement "has led us to believe that she has not been truthful to us."
"At this point in the investigation, we are having a very difficult time establishing a true timeline," Adkins said. "We are looking for the public to help us. We need teachers. We need doctors. We need store clerks. We need anyone who has seen this girl in the last week, the last month. Anything they feel is important for us to know, we need the public to call us."
Adkins told reporters earlier Monday that it is unlikely Zahra had run away, and police said over the weekend that the possibility that she was abducted by a stranger was "less likely than once anticipated." A ransom note was found at the house, Adkins said Monday afternoon, but "We are questioning the validity of that note."
Zahra is described as being about 5 feet 1 inch tall and weighing 85 pounds. She has brown hair and blue eyes, and according to CNN affiliate WCNC, she's a cancer survivor.
The girl uses a prosthetic leg and hearing aids. The hearing aids have been found, but not the prosthesis, Adkins said.
Elisa Baker was arrested Sunday morning on four counts of writing worthless checks, said Eric Farr, a spokesman for the Catawba County District Attorney's office. No attorney was listed in court papers, he said.
Farr said she faces other charges in different counties, including a felony larceny count and other bad-check charges. She is being held on $31,500 bail.
Adkins said Adam Baker faces similar charges, but police have held off serving an arrest warrant while he cooperates with police.
Adkins said Sunday that a small fire had been reported at the residence the morning Zahra is thought to have vanished. He said "some evidence" was recovered from the scene, but would not elaborate on what connection the fire may have with the investigation.
The FBI is assisting Hickory police in the investigation, officials said. Authorities ask anyone with information to contact the Hickory Police Department.
HLN's Natisha Lance contributed to this report.