There was fierce criticism of the Rt Rev James Newcome for providing the reference, which he withdrew.
The Church of England launched a formal investigation into why Bishop James provided the reference for former Carlisle Cathedral Canon Robert Bailey, who was jailed for eight years for the child sex assaults.
The 67-year-old Bishop both withdrew the reference and issued a "heartfelt apology".
Anti-abuse campaigners called for his resignation.
The Diocese of Carlisle today issued this statement: "Following the conviction of Robert Bailey last year and criticism of the reference supplied by the Bishop of Carlisle, James Newcome, the National Safeguarding Team, NST, carried out an investigation into the bishop’s conduct according to House of Bishops guidelines.