The employee is believed to have hacked into the systems searching for information on Ian Huntley, the man accused of the murders, and his fiance, Maxine Carr.
A spokesman for the Home Office, which is responsible for the CRB, said, "We cannot comment on the details of this because it is an internal matter."
The spokesman did confirm that the CRB's IT system had identified the employee, who had tried to access information that he or she was not entitled to.
"At no time was the employee in a position whereby they could access any confidential police records," he added.
The CRB, which came into operation in March, was set up to enable employers to identify candidates who would be unsuitable for certain types of work, especially that involving contact with children or other vulnerable people.
However, delays in processing criminal records checks have placed the bureau under increasing scrutiny, particularly with the new school year due to start next week.
The Home Office spokesman blamed the delays on the volume of enquiries received but confirmed that the Government had recently redeployed 100 staff to work on record checks in the education sector.
He said, "We are working hard to ensure that all teaching staff who need full disclosure checks prior to the start of the new term will have them."
The bureau is a partnership between the Home Office, the Department for Education and Skills and IT services giant Capita.