Simon Byrne was responding to claims from some unionists that prosecutions will not be possible once six months have elapsed from the time of the event in June.
Mr Byrne has also revealed that he intends to establish a new community relations taskforce in response to public concerns around how police had enforced Covid-19 regulations at some public events in the summer.
Last month, the Policing Board questioned whether the PSNI’s approach to Black Lives Matter protests was “unlawful” and if the issuing of fines to participants took due consideration of their right to protest.
The PSNI is investigating whether Sinn Fein representatives such as deputy first minister Michelle O’Neill were in breach of Covid-19 regulations by attending the funeral of IRA veteran Mr Storey in west Belfast at a time when strict limitations on numbers were in place.
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Ms O’Neill has still to be interviewed by police on the matter.
Her legal representatives continue to communicate with officers around agreeing a date and time for the interview.
Breaches of the regulations are summary offences, which fall within the jurisdiction of the magistrates’ court.
Ordinarily there is a statute bar that means a charge must be issued or a summons served within six months of an alleged offence for the court to retain the jurisdiction to deal with it.
Mr Byrne told the Policing Board that he had been liaising with the Public Prosecution Service (PPS) about triggering a long-established mechanism that allows for a case to the lodged with the court authorities before a decision to prosecute had been taken.
That would enable police investigations to continue beyond the six-month statute bar.
“I want to assure all board members and indeed the public that speculation that we’re running down the clock in relation to the Storey funeral investigation is misplaced and I have personal assurances from the Prosecution Service about how the time dimension will be managed within normal practice and procedure,” the police chief told the board.
Announcing the new task force, Mr Byrne added: “I do also recognise that events across the summer have shown the depth and breadth of public emotion which is palpable.
“Different communities have seen at different times frustration, concern indeed hurt about how we policed a variety of things from funerals to parades to protest.
“So I recognise that working with yourself (the board) it’s my duty and our duty to maintain and improve public confidence.”
He added: “I want to commit to making improving community engagement a key priority for next year.”