THIRTY-six republicans who received "comfort letters" from the British government after their statuses were changed from wanted to not wanted are linked to 136 incidents, police said.
On The Runs (OTRs) were suspects fleeing potential imprisonment for murders and other serious offences during the Troubles.
A special unit established by the PSNI is reviewing the cases of 228 considered under the scheme.
Chief constable George Hamilton said: "These individuals are linked to many serious crimes throughout the period of the Troubles.
"The focus of the team is on 36 individuals, referenced within the report of Lady Justice Hallett, whose status had previously been changed from wanted to not wanted.
"The team has reviewed 136 incidents linked to those 36 individuals."
Lady Justice Hallett, who examined the OTRs scheme for the Government, noted that a comparatively high number of suspects had their statuses changed to not wanted between February 1 2007 and October 20 2008.
The contentious process, agreed between Sinn Fein and the last Labour government, saw letters sent to republicans informing them they were not being sought by the authorities in the UK.
Police were asked to review the evidence to assess if they were either wanted or not at that particular point in time.
Those who were not being actively pursued due to a lack of sufficient evidence received a letter from the Government informing them.
Sinn Fein said the concession was necessary to restore confidence in the British government's commitment to deal with OTRs to ensure the success of arms decommissioning, Lady Hallett reported. The government said it was a statement of fact carrying no future guarantees.
Police have since revealed that OTRs who received letters were linked to hundreds of murders.
Some unionists claimed it was equivalent to a get out of jail free card, something the British government has denied.
Ulster Unionist Fermanagh and South Tyrone MP Tom Elliott said: "Were these reassurances letters sent out because of security measures? Or were they issued due to a political deal, that happened to coincide with the return of devolution to Northern Ireland?
"In the space of 20 months, 36 OTRs had their status changed from wanted, to not wanted. Explanations need to be forthcoming from the British Government and the PSNI."
Details of the scheme, which followed the 1998 Good Friday Agreement, emerged after the collapse of a case against a man accused of the IRA's Hyde Park bomb in 1982 - an attack that killed four soldiers - after he received a letter in error.
Following the controversy, the PSNI is reviewing its initial assessment of all 228 individuals to see if any other mistakes were made or if fresh evidence has emerged.
Chief Constable George Hamilton, in a response to the Policing Board, said he could not estimate when the probe would be completed.
He said: "This is primarily because of the potential volume of incidents that will need to be examined by the PSNI in order to establish whether there are credible opportunities to bring any of these offenders to justice."
Lady Justice Hallett said the change in status under the scheme may be because evidence no longer existed and/or in part because the police's Operation Rapid team doing the investigation in 2007/08 may have applied a higher threshold to categorise someone as wanted than previously.