Sei Jeremiah Gakuen

Nishina Hitoshi is an agent of Secret Police and missioned to investigate the murder case in the Saint Eremiya girls school. Five girls of the school died from the destruction of soul. The destruction of soul is a very rare phenomenon, so it's entirely extraordinary that it happens at 5 girls at the same time in a place. To figure out the case you get a job of chemistry teacher in the school, with your standing concealed. And a girl-partner Kamishiro Izumi gets an entrance into the school as a student. You and your partner work severally and exchange information sometimes. St. Eremiya is a mission school and the president and the chief teacher are nuns.

[Edited from Helmut review]