The girl, Maya Thomas, died that evening. Her mother, India Miller, 27, and stepfather, Sean Scott, 45, have been charged with first-degree murder, making fictitious reports to police, endangering the welfare of a child and related offenses. The charges are allegations; the case has not been proven in court.

Police records describe how officers initially pursued Miller and Scott’s account that Maya had been hit by a vehicle outside their Swedesboro Avenue home. Miller said she heard tires screeching, while Scott said he found Maya collapsed near a shed, according to the complaints.

Officers looked for damaged cars and sought video from nearby locations, including Loudenslager Elementary School and the fire department. At about 1:48 a.m., the school principal joined the effort to access surveillance footage. An officer went to the superintendent’s home when the principal could not reach him, dispatch logs show. Police also asked the fire chief to provide access to the department’s cameras.

A preliminary review found no vehicle traffic in the area during the period the couple described, according to the complaints.

At the hospital, medical staff reported facial trauma, bruising and injuries to Maya’s vaginal area that they said were inconsistent with a vehicle strike. A 4-year-old sibling told investigators that Scott had hit Maya in the face and eyes, the complaints allege.

Police obtained a warrant to search the home. Investigators described finding the house in disarray, with disconnected smoke detectors and removed batteries. They also reported children’s clothing in an upstairs bathtub and what they believed to be blood on bathroom tile, a floor-cleaning device and cleaning supplies.

Maya died at 6:42 p.m. on Oct. 13, after her mother and stepfather had been taken into custody, according to the account of the investigation.

An autopsy by the medical examiner serving Gloucester, Salem and Cumberland Counties found multiple blunt-force injuries, including trauma around both eyes, a swollen-shut left eye, abrasions on Maya’s lower body, a ruptured colon and several broken ribs. Some of the ribs were in different stages of healing, the complaints say, suggesting injuries over time.

The New Jersey Department of Children and Families said it received a referral from the Gloucester County Prosecutor’s Office on Oct. 13 concerning allegations of severe physical abuse. The department is investigating, spokesperson Jason Butkowski said. He said Maya’s younger sibling was removed from the home and placed in emergency care, but declined to provide additional information because child-protection investigations are confidential.

Maya was not enrolled in Paulsboro Public Schools, according to a letter posted by district Superintendent Phillip C. Neff Jr. Her death has also prompted calls from state legislators for greater oversight of homeschooling, according to public reporting on the case.