The Catholic Church in Adelaide says an investigation has found there is no substance to allegations made by Traditional Anglican Archbishop John Hepworth against a parish priest.

Archbishop Hepworth has alleged he was sexually abused when he was a young man by Monsignor Ian Dempsey.

The investigation was conduced by prominent Adelaide lawyer Michael Abbott QC.

The Catholic Church also says Mr Abbott found there was no basis for any criticism of how it dealt with Archbishop Hepworth's allegations.

Monsignor Dempsey says he is relieved at the outcome of the investigation.

He says it has been the most difficult time of his life.

"Very much relieved that the truth has finally come out and justice has been served," he said.

"It was a very extensive inquiry by Mr Abbott and it has come out with the truth, for which I am very relieved."

But independent Senator Nick Xenophon says the investigation is not credible because Archbishop Hepworth refused to take part.

Senator Xenophon named Monsignor Dempsey in Parliament in September because of what he claimed were delays by the Catholic Church in responding to the allegations.

"This inquiry should not have been progressed unless there was a fair and robust and transparent process that John Hepworth was comfortable," he said.

"John Hepworth participated fully in the Melbourne process over allegation involving other priests.

"That process was fair, chalk and cheese compared with the way the Adelaide archdiocese has dealt with these particular complaints."

Archbishop Hepworth says he refused to take part in the Abbott investigation for a number of reasons, including that he did not know its terms of reference and that he was expected to pay for his expenses.

The Catholic Church says it is not making the investigation findings public because they contain sensitive information.

Michael Abbott QC has defended his investigation and says his conclusions were justified.

"We've interviewed all these witnesses, we've looked at all these records, we've endeavoured to tease and examine all the claims and allegations that Archbishop Hepworth has made," he said.

Obviously I would have wanted him to participate but the act that he's now saying I haven't participated therefore the investigation's flawed to me is, well I don't agree with that."