Amayo no Mayoi Neko

On his way home from work, the protagonist Shin meets a girl who is sheltering from the rain. The rain had soaked the girl's uniform, prompting the good-natured Shin to give her the umbrella he had with him. But she doesn't use the umbrella at all. Rather, she chooses to follow him. Is this some new kind of stalker? Shin ran away in an attempt to get rid of her, but...