Sakurasou no Pet na Kanojo

From MangaHelpers:

After being kicked out of the main dorms for bringing in a stray cat, Kanda Sorata is forced to live in the smaller Sakura Halls where problem students are sent to live. Although he doesn?t mind his roommates, Sorata can?t wait to move out of Sakura Halls. But when Shiina Mashiro moves into the dorm, everything changes. Mashiro is an artistic genius who, at a young age, won many awards for her skills, but due to her childhood being so focused on art, she has no common sense and social skills. Forced to take the role of taking care of Mashiro, Sorata learns about himself and begins on a path of self improvement.