Ian Huntley, who has been charged with the murders of Holly Wells and Jessica Chapman, worked as a school caretaker in Soham, Cambridgeshire, while his partner Maxine Carr, who is charged with attempting to pervert the course of justice, was a teaching assistant in the girls' class.
East Renfrewshire is at pains to stress that it is not acting because it has any suspicions of staff or has concerns that procedures were not followed in hiring them.
Its aim is simply to provide public reassurance.
All new employees now have to submit birth certificates before they are appointed to eliminate the possibility of false names being used.
Owen Taylor, convener of East Renfrewshire, said: "We recognise the dedication of our staff and the valuable work they do, but we also recognise at this tragic and disturbing time that many parents may seek extra reassurances and it is only right that we give these."
All authorities will also have access to Disclosure Scotland if they want to vet potential employees, although it will only hold records of those with criminal convictions. Non-conviction information can be passed on from local police records, however, where this is felt to be appropriate to the job application.
The disclosure system, established in April, is particularly aimed at voluntary organisations. It is estimated that 100,000 volunteers work with children and vulnerable adults in Scotland, and ministers are providing pound;1 million a year to cover the costs of checks.
In addition, an index of adults unsuitable for working with children will provide information for employers where there is no criminal conviction.