Fatal Confession: A Father Dowling Mystery (1987)

Frank Dowling is a priest whose views on religion are somewhat liberated and also has a penchant for solving mysteries. He now has to solve the mystery of a young man who's obsessed with finding his natural parents. When he steps out on the ledge of a building, threatening to jump unless he's told who his parents are, Father Dowling is called to try and talk him down but unfortunately he jumps and Father Dowling, feeling responsible, looks into it. He learns that he may have been murdered, but he still has to find out how, why, and who.