Baggott – who quits in September – last week was forced to apologise to the relatives of Hyde Park bombings when IRA man John Downey walked to freedom from court in London after he received a so-called letter of ‘amnesty’.
The Northern Ireland Office letter said neither the PSNI nor the Metropolitan Police were looking for him.
However, it was subsequently revealed that the Metropolitan Police were in fact looking for him over the 1982 Hyde Park atrocity- and the PSNI knew about it.
It was later revealed there was a computer error.
Today, the Chief Constable gave a behind-closed-doors private briefing to the Policing Board members about the debacle which has engulfed his force.
Board chairman Anne Connolly said: “The chief constable told the Board that the PSNI actions in this process were legitimate and lawful and that the PSNI do not believe the letters confer an amnesty.”
He also pledged that the PSNI would co-operate with the Police Ombudsman who is now investigating the role of senior police in the Downey case.
Letters were sent to about 200 people by the Northern Ireland Office (NIO) after a search of police records to identify if they were wanted in connection with crimes.
Prime Minister David Cameron has launched a judge-led independent inquiry into the row.
The Board reviewed its files for information about on-the-runs.
Ms Connolly added: “It is not possible to determine from the documents held the level of detail provided to the Board and whether information on the role and work of the OTR unit was briefed to the Board.
“The first detailed record which provides substantive information on the PSNI approach to the review of information is in 2010 when questions were raised in Board public session and correspondence is received from assistant chief constable crime operations.”
A police spokesman said “The chief constable Matt Baggott confirmed to the Policing Board today that the PSNI acted legitimately in carrying out their role in this process and that he would be complying fully with the judge’s review and with the Police Ombudsman investigation.”
Downey, 62, from Creeslough, in Co Donegal, had pleaded not guilty to the murder of four soldiers from the Household Cavalry who died in the Hyde Park blast on 20 July 1982 along with seven of their horses.
The bomb had been concealed in a car and was detonated as the soldiers rode past on ceremonial duties.
Oyster farmer Downey was detained at Gatwick Airport in May 2013 en route to Greece and spent nine months in custody awaiting trial.
But he dramatically walked free after an Old Bailey judge stopped the case because a letter had been erroneously sent to him from the Government prior to his arrest saying he was not wanted by the police.
The message, which gave no guarantee that future evidence would not emerge linking him to Hyde Park, was sent as part of political talks between Sinn Fein and Tony Blair’s administration linked to the consolidation of the peace process.
The revelation that many others received similar letters prompted outrage from victims of terrorism who branded them “get out of jail free” cards.
First Minister and DUP leader Peter Robinson said he had been kept in the dark and threatened to resign.
However, withdrew the threat after Prime Minister David Cameron ordered a judge-led inquiry.
Belfast Daily revealed last week that Mr Robinson and his deputy Nigel Dodds knew about the OTR deal.
According to the memoirs of the then Prime Minister Tony Blair’s chief of staff, Jonathan Powell, they told him they spent three hours briefing their party leader Ian Paisley about what they described as the “unpopular” scheme.