46-year-old Jacintha Saldanha, who was found in nurses' quarters near the private King Edward VII's Hospital in central London on Friday, left three notes before she died, a police officer told the hearing.
The Indian-born mother-of-two also had injuries on one of her wrists.
Police said there were "no suspicious circumstances" surrounding her death.
Detective Chief Inspector James Harman told the opening of the inquest: "Jacintha Saldanha was found by a colleague and a member of security staff. Sadly she was found hanging. There were also injuries to her wrist."
"The London Ambulance Service was called to the scene."
Two notes were found in her room and another was among her possessions, Mr Harman told the hearing at Westminster Coroner's Court, without revealing their contents.
Police are also looking at telephone calls and emails to see if they shed more light on her death, he said.
Scotland Yard will "in the very near future" be in contact with Australian police to ask them interview witnesses there, he added.
Ms Saldanha's husband Benedict Barboza and two teenage children did not attend the hearing.
The full inquest - which could record any one of a number of possible verdicts including suicide or misadventure - will be held in March 2013 after toxicology tests and further investigations.
In England, inquests are held to examine sudden or unexplained deaths. They set out to determine the place and time of death as well as how the deceased came by their death. They do not apportion blame.
Setting a provisional date of March 26 for the next hearing, coroner Fiona Wilcox told 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."
Australia's media watchdog on Thursday opened an investigation into the prank call.
The Australian Communications and Media Authority (ACMA) said its probe was into the broadcaster, 2Day FM, and not presenters Mel Greig and Michael Christian who have borne the brunt of worldwide anger.
The station's right to broadcast could either be cancelled, restrictions put on its licence or it could be fined.
Ms Saldanha, a nurse originally from near Mangalore on the southwest Indian coast, was found dead Friday.
Three days earlier she answered a prank call to the hospital made by two Australian radio presenters impersonating Queen Elizabeth II and her heir Prince Charles, William's father.
Ms Saldanha put the call through to a nurse who divulged details of Kate's condition as she recovered from acute morning sickness.
The radio station has pledged at least 500,000 Australian dollars (approximately Rs 2.7 crore) to help the grieving family, but British lawmaker Keith Vaz, who has been acting as their spokesman, said the broadcaster had not done enough.
"There has been no written apology, no request for a meeting with the family, and no attempt to travel to the United Kingdom to express contrition," he said, according to ABC radio which interviewed him.
He also questioned how the network arrived at the figure of $500,000.
British Prime Minister David Cameron told parliament on Wednesday that the death is a "complete tragedy."
"There will be many lessons that need to be learned," he said, adding that the family should be given "the time and space to grieve".
Kate is continuing to rest and William attended the British premiere of "The Hobbit: An Unexpected Journey" on his own on Wednesday.
The royal couple, who are expecting their first child, have said they were "deeply saddened" by her death while their spokesman said that the palace had at no stage complained to the hospital about the hoax call incident.
The hospital has also said that it gave Ms Saldanha its full support.