Looking at the synopsis and LZ's question is a bit different, the investigation of the case in the film is a detective, not the two FBI?

Film synopsis:

The story takes place in a small town in the Midwest of the United States in the 1950's. Because it is far away from the city, this place has a quiet environment, coupled with the pure and simple people and the people with the hard work in exchange for the richness of the isolated town is not lonely at all.

The story is set in a small town in the Midwest of the United States in 1950, far from the city.

However, a sudden murder broke the peace of the town, and before people woke up, several similar murders occurred one after another, and the dead were underage children. The town's righteous people are outraged, they hate the murderer's cruel and despicable crimes, and curse the murderer will be punished.

At this point, the town's Inspector Shelly (Jack Nicholson) has a muted reaction to what's going on, and all he can think about is how to retire and enjoy his life in peace. Despite his worldly savvy and notoriously difficult temperament, he is approached by the mother of a murdered child who places her hopes of punishing the murderer squarely on his shoulders. The Inspector is ultimately moved by the mother's sincerity and is determined to do his utmost to help her fulfill her wish.

As the investigation deepens, the case becomes more and more complex, and heavy traps several times endangered the detective's life. The Inspector did not shrink from this, and continued to investigate despite everything. Finally, with his incomparable courage and wisdom to make the murderer was duly punished, to honor his oath.