Nekotsuku, Sakura.

Gods (ghosts) reside in this school...
Kuji Academy's building has a vast history and boasts its vast facilities and a huge number of students.
One spring day, main character Ootsuki witnessed an odd event while helping with the entrance ceremony: Cat ears grew from the head of Ayano, a female freshman!

Another girl with cat ears appeared to apologize to the two. She introduced herself as Tsuki, the "twin god" younger sister, a guardian deity rumored to protect the school.
Tsuki explained, "My older sister possessed Ayano. That's why she grew cat ears!"

The "twin gods" true identity is that of two cat ghosts that haunt the academy. They also seem unable to get out of the school grounds.
Aki, the older sister, got tired of it. She planned to possess Ayano as a means to get out of school.

However, even while possessing Ayano, Aki is unable to leave! As Aki's wishes cannot be fulfilled, Ayano remains possessed.
Thus, Ootsuki's new school year starts as he tries to find a method to grant Aki's wish with the help of his good friend Renka and the occultism enthusiast Yayoi.