The Traditional Anglican Archbishop who claims to have been sexually abused by a serving priest has filed a complaint with South Australian police.

Archbishop John Hepworth claims abuse by Catholic priest Monsignor Ian Dempsey decades ago when they were training for the priesthood.

A Catholic Church-commissioned investigation of the claims by Michael Abbott QC has cleared Monsignor Dempsey of any wrongdoing, finding there was no substance to the claims.

Archbishop Hepworth has now been to police in Adelaide to make a complaint.

"I am formally requesting the police to examine the matter," he told reporters.

"It was never my intention to go beyond the processes of the church, but I have been left with no option.

"I very much regret that I'm having to do that."

Archbishop Hepworth refused to take part in the investigation conducted on behalf of the Catholic Church.

He says he has a hostile relationship with Mr Abbott and that the rejection of his allegations has forced him to take the matter further.

But Mr Abbott says several attempts were made to involve Archbishop Hepworth in the investigation.

"I see no reason why I should have disqualified myself, and I don't think anything Archbishop Hepworth has said would cause me to disqualify myself," he said.

The detailed findings have not been made public.

Independent Senator Nick Xenophon used Parliament back in September to name the priest involved in the allegations and has condemned the findings of the church's own investigation.

He argues it is not credible because Archbishop Hepworth refused to take part.