Fergus Dunlop, Senior Constable of St Saviour, said concerns had been raised with the States prior to Wednesday's collapse at Perelle.
He argued that it was his role as a senior chief constable to "talk about topical issues and by definition that involves issues that are political".
In his letter, Mr Jones asks what discussions took place between the press office, the chief constable and senior officers after the media showed interest in the incident.
These will be significantly streamlined to support a single service, a single Chief Constable and one senior management team.
Belfast's senior police commander, Assistant Chief Constable Duncan McCausland, said both the marchers and those opposed to the parade had been "constructive and positive in their approach".
BBC: NEWS | UK | Northern Ireland | Parade passes off peacefully
She said the Police Service of Northern Ireland's Chief Constable Matt Baggott believed senior members of the Ulster Volunteer Force (UVF) had been involved in orchestrating the violence, but without the authority of the group's leadership.
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Earlier on Monday, Northern Ireland's chief constable, Matt Baggott said senior members of the UVF in east Belfast - as individuals - had been "increasingly orchestrating" some of the violence.
Operational responsibility for the day-to-day policing that matters most to people on the doorstep (crimes against the person, burglary and anti-social behaviour) remains with senior police officers headed by the chief constable.
Professor Rea is chairman of the Northern Ireland Policing Board which handles some of the most sensitive issues facing policing and holds PSNI Chief Constable Hugh Orde and his senior officers to account.
The Superintendents' Association, which represents senior officers below the rank of chief constable, argues that officers could patrol alone, rather than in pairs, and detectives could work in uniform, rather than in plain clothes.
Police investigating the murder were so alarmed about heavy drinking by the crew while ashore that the senior officer wrote to Hampshire's Chief Constable to highlight the issue and the warning was passed to military authorities.
The two former senior officers who want the audit office investigation are Alan McQuillan, a former assistant chief constable who retired in 2003 and Norman Baxter, who was one of the PSNI's most senior detectives when he retired in 2008.
Four senior police officers - including Northamptonshire's chief constable and deputy chief constable - are being investigated over misconduct claims relating to Staffordshire Police's investigation into the murder.
It currently takes about 25 years for a newly recruited constable to work their way to the most senior level, a process that is thought to deter talented people from other professions from joining the police, our correspondent adds.
Instead, the chief constable's response has been to appoint a senior detective from Merseyside to advise Detective Superintendent Brian McArthur, who is heading the Omagh investigation.
But the Police Federation, the policemen's trade union, is strongly opposed to fast-track entry which would give high-fliers on short-term contracts accelerated promotion into senior ranks without having to serve on the beat as a constable.
Deputy Chief Constable Sean Price said while the force was at record size, not as many senior officers had been recruited as hoped.
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