Lilith

An intense night battle between kunoichi clan leader and evil biblical spirit Lilith ends with kunoichi falling into coma state.
A cat gets into an ordinary student Koketsu room, transforms into a girl and claims that Koketsu got her master kunoichi spirit and must help her master and defeat Lilith. The problem is that nothing is known about Lilith but the name and together they set to uncover its secrets.

[From vndbreview]