He said: "I believe Wiltshire Police has taken on more than its share in relation to this national investigation.
"I have consistently said that I will not commit to an additional financial burden, potentially running in to hundreds of thousands of pounds, that would detract from policing in the county.
"I fully understand the position of Sir Edward's supporters in seeking an independent review to determine the veracity of the allegations but there can be no certainty a review would deliver this outcome.
"My role is to hold the force to account - which I have done, to ensure resources are directed to preserve the community policing for 700,000 local residents and to provide a good quality, efficient, service that keeps the county safe.
"I remain satisfied that Wiltshire Police has applied to the letter the national advice issued by the College of Policing. This view was reinforced when the Home Office part-funded the investigation on the basis of a supportive review by Her Majesty's Inspectorate of Constabulary. No further review of the investigation is required."