Inutsuki-san

A girl wants to kill her classmate as revenge for vicious bullying. She decides on "ko-doku", a cruel poisonous curse that requires a sacrifice, as the method of killing....... This is the start of a supernatural story about occult incidents that happen behind the scenes at an all-girls high school, and the activities of an unorthodox dog-possessed girl, Ayumi Kusunose.

(Source: Square-Enix Novels)