Tsun na Megami-sama to, Dare ni mo Ienai Himitsu no Kankei.

Hazuki is the student body president at the all-boys' school Kuronami High. However, due to a recent decline in enrollment, Kuronami is set to merge with Shiramine Girls’ School. During the first year of the integration, both schools will retain their respective student council presidents until the end of their terms. The president of Shiramine High is none other than the cool, beautiful, almost flawless "Ice Goddess," Yukimiya Hyouka — a girl of breathtaking beauty. As part of the integration process, Hazuki moves out of his family home and begins living on his own. To his shock, his new neighbor turns out to be Yukimiya Hyouka herself! Now living next door to the "Ice Goddess," Hazuki stumbles upon an unbelievable secret about the girl everyone thought was perfect. (Source: Shueisha, translated)