Scotland Yard has submitted a file to the Crown Prosecution Service relating to the hoax call made to the hospital where the Duchess of Cambridge was treated for morning sickness.
Nurse Jacintha Saldanha, 46, was found dead after she transferred the call from two Australian radio presenters to a colleague who then described Kate's condition in detail.
The Crown Prosecution Service (CPS) will now consider whether any potential offences may have been committed, Scotland Yard said.
Saldanha, a mother of two, was found dead in her nurses' quarters at London's King Edward VII's Hospital by a colleague and a security guard on December 7.
Three days earlier she put through a call from Sydney presenters Mel Greig and Michael Christian, believing they were the Queen and Prince of Wales.
Greig and Christian spoke of their grief on Australian television soon after the nurse's death.
They said their prank had prompted 'a tragic turn of events no one could have predicted or expected'.
A Scotland Yard spokesman said: 'Following the death of Jacintha Saldanha, officers have liaised with the CPS as to whether any criminal offences had been committed in relation to the hoax call made to King Edward VII Hospital in the early hours of Tuesday December 4.
'On Wednesday December 19, officers submitted a file to the CPS for them to consider whether any potential offences may have been committed by making the hoax call.'