The Police Ombudsman is investigating a complaint from the family of journalist Lyra McKee.
Ms McKee, 29, died after she was shot in April 2019 while observing a riot in Londonderry's Creggan estate.
The complaint from Ms McKee's family relates to aspects of the policing operation which took place in Derry on the night of her death.
It is understood the complaint relates to the decision of the Police Service of Northern Ireland (PSNI) to search a house in Creggan on 18 April 2019.
Nothing was found in the search and while it was happening, rioting broke out during which Lyra McKee was shot dead.
In a statement, the McKee family said: "Whilst we hold Lyra's killer and their associates completely responsible for her murder, we have asked the police ombudsman to investigate the aspects of the policing operation on 18 April 2019.
"The police ombudsman investigation is completely separate to the ongoing murder investigation. We consider this a very personal family matter and have no further comment."
The New IRA is believed to have been formed between 2011 and 2012.
It followed the merger of a number of smaller groups, including the Real IRA, which itself was born out of a split in the mainstream Provisional IRA (PIRA) in October 1997 over Sinn Féin's embrace of the peace process.
'Difficulties gathering evidence'
Details of the complaint emerged as the police say they know who killed Lyra Mckee, but can't give an undertaking that her killer will be brought before the courts because of difficulties gathering evidence.
PSNI Det Ch Supt Raymond Murray acknowledged the complaint had been made but defended police actions.
"The ombudsman will conduct their investigation and it will come to its own conclusion.
"What I will say is that the officers acted in good faith with the information at the time. That is all we can do," he said.
Locals say the search provoked a riot, during which Lyra McKee was shot by a dissident IRA gunman firing at police lines.
In a separate development, SDLP MLA and policing board member Dolores Kelly accused the PSNI of failing the people of Northern Ireland.
She has criticised the PSNI for not catching dissident republican killers in the high profile murders of Lyra McKee and Jim Donegan, 43, who was shot in west Belfast in December 2018.
"I think the biggest test in terms of adequacy of the police response lies in the conviction of the people responsible and to date, unfortunately, in both cases, no one has yet been brought before the courts, either directly charged with the murder or assisting those responsible.
"I think not only will people be disappointed but they will be angry that that no one has been charged."
But Det Ch Supt Murray defended the police response to the murders of Ms McKee and Mr Donegan.
"Those investigations are very far from over and so I do feel in all honesty that these remarks potentially are premature.
"These investigations still have quite a considerable way to travel. Dissident republican murders are extremely difficult. I will go so far as to say we operate in one of the most challenging investigative environments in Europe."
Identity of the killer
In relation to the Lyra McKee murder, Det Ch Supt Murray revealed police know the identity of her killer.
"We certainly believe that we do know who pulled the trigger and who murdered Lyra McKee on that horrendous night in Creggan.
"I think it would be a failure of policing if we did not do everything in our power to bring people before the courts. We have to find the evidence.
"We have to try to get the evidence. It is incredibly difficult."
Asked if he was convinced that someone will be brought before the courts and charged with Ms McKee's murder, he said: "Those are not undertakings I give families. I don't think it is fair.
"I think it raises expectations unnecessarily. What I will say is I am convinced my officers will do everything we reasonably can to bring people to the courts. "
The Police Ombudsman for Northern Ireland confirmed it has begun an investigation of a complaint it received about aspects of policing in Derry on 18 April, the day Ms McKee was shot dead.
A spokesperson for the ombudsman said it will "look at aspects of the policing operation in the Creggan area of the city that day".
It is understood this includes examining why police decided to raid a house in Creggan.
Eamonn McCann, a councillor for Derry City and Strabane District, also raised questions about the police operation in Derry that night.
He said: "People find it very difficult to understand why there was such a large force of policemen and armoured vehicles in the area that night. And to say that is not for a moment to excuse the sheer madness and the disregard for other people's lives involved in the actions of the New IRA."
Commenting on the search operation, Det Ch Insp Murray said: "The officers who commissioned the search, I fully support them in commissioning the search based on the information that they had at the time. They acted in good faith to keep people safe.
"The reason for the murder of Lyra Mckee lies with the New IRA, their apologists , the man who pulled the trigger and those who assisted him that night."
In relation to Ms McKee and Mr Donegan's murders, the PSNI said police had "pursued" over 3,000 investigative actions, arrested over 30 people, and searched over 40 premises.
So far no one has been charged with either murder.