“I think you are going to see many other attorneys general do the same,” Ms. Conroy said.

Mr. Morrisey’s office began its investigation into the church in September, after the explosive Pennsylvania report last summer alleging that bishops and other church leaders covered up widespread child sexual abuse over several decades. The lawsuit filed on Tuesday says that, in at least five instances over several decades, the diocese put credibly accused priests back into ministry with children or did not conduct proper background checks on school employees.

In one case, Father Patrick Condron, who was employed at a diocesan school in the 1980s and who later admitted to sexual misconduct against a student, was returned to ministry at an elementary school from 1998 to 2001, without parents of children at the school being informed of his history.

Mr. Morrisey said that he was seeking a permanent court order to block the Catholic Church from continuing such conduct, and that one goal of the lawsuit was to “dramatically increase transparency” within the church.

He did not rule out the possibility of additional criminal action by the state; he said any evidence of criminal wrongdoing would be passed on to appropriate law enforcement officials.

The diocese of Wheeling-Charleston “strongly and unconditionally rejects” the lawsuit’s allegation that it is not “wholly committed” to protecting children, a diocesan spokesman said in a statement on Tuesday, adding that some of the allegations in the complaint “are not accurately described.” The findings of the church-led investigation into Bishop Michael J. Bransfield, who led the diocese from 2005 to 2018, have not yet been made public.

Mark E. Chopko, whose firm Stradley Ronon Stevens & Young represents the diocese in West Virginia, pointed out in an email that the lawsuit is administrative, not criminal, and that the state is seeking “unspecified” fines or civil penalties, rather than building a case to arrest the bishop.

Religious institutions are not usually subject to rules governing consumer protection, in part because they might be protected by freedom of religion, said Nicholas P. Cafardi, a prominent canon lawyer in Pennsylvania.