This is despite the discovery of hundreds of pornographic photographs of young men being found on Father Pearson's office computer.
Pedophile Task Force detectives found the photographs, and another image of him carrying an AK47 assault rifle, when they examined his church-owned office computer hard drive.
The assault rifle photograph was taken in Afghanistan during one of Father Pearson's frequent visits. He has remained in the war-torn location for most of the past year.
Detectives launched the investigation into Father Pearson early last year after a file was referred to them from the Mullighan Inquiry. The file contained evidence from several young Aboriginal males and their involvement with Father Pearson at the Otherway Centre in Pirie St.
Father Pearson was heavily involved in the Archdiocese of Adelaide's Aboriginal Catholic Ministry and was chaplain at the Otherway Centre until he voluntarily stood down after Archbishop Philip Wilson and Vicar-General David Cappo were advised of the police investigation.
It is understood police could take no action against Father Pearson because investigations determined youths at the centre of the allegations were just above the legal age of consent. It is understood investigations failed to identify any of the young males in the pornographic images, which had been cropped to remove their heads.
Acting officer-in-charge of the Pedophile Task Force Detective Inspector Mark Trenwith confirmed the investigation was over. "The matter has been filed," he said.
Church officials had been asked not to commence the internal inquiry until police investigations had been completed.
Last December a church spokesman said an internal inquiry into the allegations would be conducted "as soon as practicable after the police have given approval to do so".
The spokesman on Friday said the Archdiocese would now make no comment on Father Pearson's alleged conduct with Otherway Centre clients, the pornography found on his office computer or his activities in Afghanistan.
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