A mother is still to be questioned by police after her child was pronounced dead when she carried him into a County Durham police station.
Melanie Ruddell, 39, from Castle Eden, arrived at Peterlee police station on Monday with her son Christy, two, who had been strangled.
She was arrested on suspicion of murder and was taken to a secure hospital.
Detectives are waiting for permission from medical staff to speak to her in connection with the child's death.
A family member who was concerned for Mrs Ruddell's welfare had taken her to hospital on Sunday night but she was discharged.
A spokeswoman for the University Hospital of Hartlepool confirmed that Mrs Ruddell had been taken to the A&E department on Sunday, but she was released.
Det Supt Adrian Green said a post-mortem examination carried out on Monday at Sunderland Royal Hospital confirmed the boy had died as a result of being strangled.
"This is a tragic incident which obviously has left both families concerned extremely shocked and distressed," he said.
"We believe the boy was already dead for some time before he and his mother arrived at the police station.
"At this stage we are still in the process of establishing what happened on Monday morning, and a major part of our investigation involves determining the exact location where the death took place.
"While we are not looking for anyone else in connection with the murder, we would like to hear from anyone who has information which might be useful."
Police said on Tuesday Mrs Ruddell had suffered injuries to her arms, which were believed to be self-inflicted.