Police recovered the body of a nine-year-old girl near a railway line beside a family cemetery in Tarakandi, Charjashordi Union of Nagarkanda, Faridpur, at about 9pm on 1 August.
The girl, a resident of Tarakandi, had been missing since about 5pm that day.
Police searched the area after being alerted and recovered her body near the cemetery.
Her family alleges that she was raped and murdered.
A family member said the child was unclothed when her body was recovered and that her clothing could not be found.
Assistant Superintendent of Police Mohammad Al Fahad said police initially considered the incident a suspected homicide.
He said two people had been detained for questioning.
Fahad said preliminary information suggested she may have died after being injured while playing with another child.
He said investigators were examining whether other circumstances were involved.
Police sent the body to Faridpur Medical College Hospital for a post-mortem examination.
Police said the family was preparing to file a case and that legal action would follow the investigation.