A mother accused of stabbing her three-year-old daughter and then dousing the body in acid rang police several times the day before, a court has heard.
Alia Jama's body was found at a house in Birmingham on 13 February.
Her mother Iman Omar Yousef, 25, phoned police six times the previous day to complain that people were outside trying to get into her house.
She has been declared unfit to stand trial. A jury has been asked to decide if she unlawfully killed her daughter.
They have been told to disregard any question of intent.
Det Ch Insp Tim Bacon told Birmingham Crown Court two police officers who discovered Alia's body on 13 February had been to the house, in Milverton Road, Erdington, the previous day after Ms Yousef, who had paranoid schizophrenia, made the emergency calls.
He told the court Ms Yousef, an asylum seeker of Somali origin, was convinced there were people from Leicester, where she had relatives, who were "after her" and told officers she was frightened and did not feel safe at the property.
Two officers spent about an hour-and-a-half at the address and found no evidence of anyone outside, he said.
"I am certain there were no people from Leicester or otherwise who were putting Mrs Yousef in this fear," he said.
He added she could not be specific about who these people were.
Two hours after the officers left, Ms Yousef went to a police station with her daughter and demanded to be moved to a hostel, the court heard.
She was given security advice and sent home, after being told she was not eligible for such accommodation.
The court also heard one of the police officers who found Alia's body collapsed at the scene.
In a written statement Pc Cavan O'Connell said he first noticed a smell he thought to be sulphuric acid before spotting the body on the floor, covered in bin liners.
He said he lifted one of the bin liners which revealed the torso of a young child.
"I observed Pc (Alan) Roder walk out of the room and collapse on the landing."
The rest of the incident had been a blur, he said.
Earlier, prosecutor James Burbidge QC had said the scene was "truly a shocking sight".
The case was adjourned until Thursday.