Markey was ordained in Ireland in 1952, and documents in several court cases show he was accused of sexually abusing boys as early as the 1960s. The documents also show he had gone to treatment before coming to the U.S., and also received treatment at a Paraclete facility in New Mexico.
The New Ulm Diocese said Markey arrived in Willmar in December 1981 and did some temporary parish work. He left the diocese seven months later.
The New Ulm Diocese's lawsuit stems from a claim filed last year by a man who says Markey groped him and his two brothers at their family home in 1982, when Markey was filling in at rural churches in Henderson and Jessenland.
Markey died in 2012 while awaiting trial on child rape charges in Ireland.
An attorney for the religious order told MPR and KARE-TV that he had no knowledge of the latest lawsuit. The Diocese of Clogher didn't return an email seeking comment from The Associated Press.
But in court documents filed in another Markey case, the Diocese of Clogher said it did not assign Markey to work in Minnesota on its behalf, and it has no record of approving Markey to transfer to any program in Minnesota.
It is one of just a few cases in which Catholic officials have taken court action against others in the church.
In 2003, the Diocese of San Bernardino in California sued the Diocese of Boston for damages after church officials in Boston failed to disclose a priest's history of sexual abuse. The lawsuit, believed to be the first time one diocese has sued another, was later dropped.
Legal experts and those who have followed the issue of clergy abuse say the New Ulm Diocese may be looking for others to share the blame, as well others to share the cost if the diocese is found liable.
"This is just something that they're doing to keep the microscope off them because if the microscope focuses it's going to see what they did," said Pat Noaker, who represents the man accusing Markey of abuse.