Jacintha Saldanha, 46, a mother-of-two from Bristol, was found in her nurses' quarters by a colleague and a security guard on Friday.
There were also marks on her wrist.
Two notes were found in her room and another was among her possessions, London's Westminster Coroner's Court was told.
Detective Chief Inspector James Harman said: "On Friday 7 December Jacintha Saldanha was found by a colleague and a member of security staff. Sadly she was found hanging.
"There was also injuries to her wrist.
"The London Ambulance Service was called to the scene. At this time there are no suspicious circumstances."
Detectives are also looking into telephone calls and emails to see if they throw any light on the death, Mr Harman said.
He told the Coroner, Dr Fiona Wilcox, that Scotland Yard detectives would be in contact with their colleagues in Australia to interview witnesses to "put the best evidence before you" about the circumstances of the death.
He said: "I can expect in the very near future to be in contact with colleagues in New South Wales."
The body of Indian-born Ms Saldanha had been visually identified by her accountant husband Benedict Barboza, the court heard.
None of Ms Saldanha's heartbroken relatives were at the five-minute hearing but they were not forgotten by the coroner.
As she set a provisional date of 26 March next year for the next hearing Dr Wilcox told family representatives in the court: "I would like the police to pass on my sympathies to her family and everybody who has been touched by this tragic death."
Ms Saldanha had been fooled by the two DJs into believing they were the Queen and Prince of Wales during the prank call to the King Edward VII's Hospital in London.
She had unwittingly transferred the call from the Sydney-based station 2Day FM to a colleague, who described in detail the condition of Kate, who was being treated at the time for severe pregnancy sickness.