Northern Ireland's Policing Board is to seek an early meeting with the Chief Constable to discuss the outcome of the Omagh bomb trial.
Sean Hoey has been found not guilty of charges against him in relation to the Omagh bombing.
Relatives of the victims of the Omagh bombing have called for the establishment of a cross border inquiry into the explosion.
Some of the relatives were angry at the way the police had handled the investigation.
The trial of Mr Hoey, a 38-year-old electrician from Jonesborough Co Armagh, ended in January after 56 days.
It has been one of the biggest in Northern Ireland's legal history.
Mr Hoey denied a total of 56 charges against him. These include the murders of 29 people, including a woman expecting twins, in the Omagh bomb in August 1998.
The prosecution case relied heavily on low-copy number DNA evidence - a new and more sensitive form of testing.
But the results were robustly challenged by the defence. During the trial, experts differed on how reliable they believed the DNA tests to be. Defence lawyers also challenged the integrity of some of the police and forensic witnesses.
Mr Hoey did not give evidence on his own behalf during the trial.
He has been held in custody for the past four years.
Mr Justice Weir took just over 75 minutes to deliver his verdict and he was highly critical of the forensic evidence presented by the prosecution.
But he was not satisfied beyond a reasonable doubt that fibres found in glue used to assemble power units could be linked to the accused or to establish, as the prosecution had claimed, common authorship that the one person was involved.
Mr Justice Weir was critical of the police investigation and the forensic service of Northern Ireland. He referred to 'deeply disquieting and deliberate deception' during one period of the trial.
The judge was also highly critical of the process of bagging, labelling and recording of exhibits and hit out at the 'slapdash approach' and 'cavalier disregard' the police and some forensic experts had for the integrity of forensic items.
In a statement the PSNI said it will study Mr Justice Weir's judgment in detail and will work to ensure than any organisational or procedural shortcomings are addressed.
The PSNI said it also awaits the outcome of a Police Ombudsman's investigation who gave evidence during the trial.
