Brisbane's Catholic Archbishop Mark Coleridge is being investigated by his former archdiocese over his alleged handling of information on child sex abuse.

A complaint against Archbishop Coleridge was made by a Canberra woman who said she had a meeting with him in 2006 when he was Archbishop of Canberra and Goulburn about child sexual abuse allegations.

A spokesman for the Archdiocese of Canberra and Goulburn said an independent investigation was being conducted after the church was made aware of the allegations a few months ago.

"Discussions between the two Archdioceses led to agreement that Canberra and Goulburn would establish an independent investigation of the allegations," the statement said.

"When the complainant was invited to cooperate with the independent investigation, she chose not to engage with the process.

"She has instead chosen to take these allegations to the media, which is deeply disappointing."

The statement said Archbishop Coleridge had "cooperated with the investigation and strongly refuted the allegations".

Archbishop Coleridge was ordained a priest in St Patrick's Cathedral in Melbourne in 1974 and was named Metropolitan Archbishop of Brisbane in 2012.

He was appointed as Archbishop of the Canberra and Goulburn Archdiocese in 2006 where he remained until 2012 before moving to Brisbane.

Last week Archbishop Coleridge attended the Catholic Church summit on child sexual abuse at the Vatican and gave a sermon at a Sunday morning mass in Rome at the end of the four-day event where cited the need for more transparency and accountability from the church.

"We will not go unpunished. In abuse and its concealment, the powerful [of the church] show themselves not men of heaven but men of Earth," he said during the sermon.

"At times, however, we have seen victims and survivors as the enemy, but we have not loved them, we have not blessed them. In that sense, we have been our own worst enemy."

The woman told the ABC on Tuesday the Archbishop had dismissed her complaint at that time.

She said she had filed the complaint to Archbishop Coleridge's office, as well as the Australian Catholic Bishops Conference in December 2018.

The woman said she had been complying with the investigation.