One of three suicide notes left by nurse Jacintha Saldanha criticized staff at the King Edward VII hospital for how they treated her following the hoax call.
The Guardian reported Saldanha's husband was given typed copies of the three handwritten letters by the police.
One note is about the hoax call made by Australian DJs from 2Day FM, another details her requests for her funeral, and the third discusses her employers, the hospital, and allegedly contains criticizm of staff.
A source close to the family told the Daily Mail: "One of the letters, which is the longest, deals with the hospital and is critical in its tone.
"Needless to say, Ben (her husband) wants a full inquiry into what happened and he wants to make sure the truth comes out.
"Within the letter, Jacintha calls into question some of the treatment she received at the hospital."
The hospital has stated that Saldanha was not disciplined after she was duped by Australian radio DJs who made a hoax call to the hospital seeking information on the condition of Kate Middleton. Both nurses involved had been offered "full support", the hospital said.
During an inquest hearing on Thursday, Coroner's officer Lynda Martindill said the mother-of-two was discovered hanging in the staff quarters of the hospital and also had injuries to her wrists, AP reported.
Harman confirmed to the coroner that Scotland Yard detectives will gather evidence from Australia as part of the investigation into the tragedy.
"There are a number of emails that are of relevance in helping us establish what may have led to this death and we are also looking at the deceased's telephone contacts," he said.
"Detectives spoke to a number of witnesses, family, friends, colleagues in order to establish anything that led or may have contributed to this tragic death."
The hearing lasted five minutes and was adjourned until March 26.
More from GlobalPost: Husband of nurse Jacintha Saldanha is "angry" with Australian radio prank DJs
Meanwhile the Australian Communications and Media Authority has announced it will use discretionary powers to begin an "own motion" investigation of the call, The Sydney Morning Herald reported.
The probe could see a revocation of 2Day FM's licence, the newspaper said.