Ms McKee, 29, died after she was shot in April 2019 while observing a riot in Derry’s Creggan estate.
The New IRA has admitted carrying out her murder.
The complaint from Ms McKee’s family relates to aspects of the policing operation which took place in Derry on the night of her brutal death.
It is understood the complaint relates to the decision of the PSNI to search a house in Creggan on Thursday, April 18 2019.
Police said at the time that the search was for terrorist material it believed was to be used over the Easter weekend in 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.”
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 Detective Chief 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.Police have also been criticised for not catching the killers of Belfast-based drug baron Jim Donegan who was blasted to death times in December 2018.
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.”
Det Ch Supt Murray revealed that 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.”
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.”
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.”
Despite a number of arrests, mo one has yet been charged with Lyra McKee’s murder.
However, two men have been charged over rioting in Creggan on the night Ms McKee was murdered.
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