Nearly 1,700 priests and other clergy members that the Roman Catholic Church considers credibly accused of child sexual abuse are living under the radar with little to no oversight from religious authorities or law enforcement, decades after the first wave of the church abuse scandal roiled U.S. dioceses, an Associated Press investigation has found.

These priests, deacons, monks and lay people now teach middle-school math. They counsel survivors of sexual assault. They work as nurses and volunteer at nonprofits aimed at helping at-risk kids. They live next to playgrounds and day care centers....