"At this time there are no suspicious circumstances," Detective Chief Inspector James Harman told an inquest at Westminster Coroner's Court.
46-year-old Jacintha Saldanha was found dead on Friday last, three days after the hoax call from two Australian radio presenters pretending to be the Queen and Prince Charles.
She had transferred the call at the King Edward VII's Hospital to a colleague who detailed 30-year-old Kate's condition.
The inquest heard that Saldanha, a mother of two, was found hanging by a scarf from a wardrobe in her nurses' quarters near the hospital in central London.
Saldanha also had injuries on one of her wrists.
"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," Harman told the inquest.
He said that two notes were found in her room and another was among her possessions.
He did not disclose their contents.
Harman, however, said police were studying the notes, interviewing Saldanha's friends, family and colleagues and going through the e-mails and phone records to establish the circumstances leading to her death.
Detectives "in the very near future" would also be getting in touch with police in Australia's New South Wales state to collect "relevant evidence," he said.