The Police Ombudsman will inform the family of its conclusions today.
Ms Simpson’s death in Derry in 2020 was treated by detectives as suicide for several months.
Multiple red flags were missed before her sister’s partner, Jonathan Creswell, was eventually charged with her murder.
Creswell was found dead at home while standing trial in April.
Three women charged with helping him cover up the murder received suspended sentences.
Ms Simpson, 21, from Tynan in County Armagh, died six days after being admitted to Altnagelvin Hospital, having never regained consciousness.
Creswell, 36, had viciously beaten her before strangling her to death.
He rang 999 and claimed he had found her hanging from a stairwell.
PSNI Chief Constable Jon Boutcher has accepted there were “a number of shortcomings” in the early stages of the police investigation and has met Ms Simpson’s family to apologise.
He told a meeting of the Policing Board in August that the PSNI had displayed a mindset which had not been “professionally curious enough”.
Before Cresswell’s arrest, several people, including relatives of Ms Simpson, had raised concerns about him.
He had a previous conviction for an attack on a woman in 2010.
The Police Ombudsman’s investigation resulted in a file of 1,400 pages being sent to the PSNI.
It found misconduct by a number of officers, with their cases dealt with by the PSNI’s Professional Standards Unit.
The investigation followed a number of complaints lodged by Ms Simpson’s family, related to the fact that police did not treat her death as murder at an earlier stage.
They are bringing a civil action against the PSNI.
A number of further complaints have been made to the Ombudsman recently and are now under investigation.
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