The document was released minutes after the girl's mother, Jerice Hunter, had her first court appearance, during which she proclaimed her innocence.
Hunter was arrested Monday on a felony count of child abuse after police say they received new information in the case. They declined to say what that information was, but the court document detailed an interview they conducted with Hunter's 13-year-old daughter.
The teen told police that Hunter had instructed her to lie about her sister, Jahessye Shockley, being missing, the document said. She also said Jahessye had been abused and had black eyes before she disappeared.
Jahessye was last seen Oct. 11 after Hunter said she went out for an errand and left the girl in the care of three older siblings at their Glendale apartment.
At a news conference Monday, Glendale Police Sgt. Brent Coombs said authorities do not expect to find Jhessye alive. He also said Hunter is the "No. 1 focus" in the investigation into the girl's disappearance.
Hunter has maintained her innocence and criticized the Glendale Police Department's investigation.
"We feel that law enforcement is not active in finding Jahessye and that they're more active in persecuting me instead of finding out where she is," Hunter said in October.
State Child Protective Services removed Hunter's other children, including a newborn, from her apartment last month but declined to say why. Glendale police said they had no part in the decision to remove the children.