Honjitsu mo Hare, Ijo Nashi

Narumi is a remote and peaceful island (modeled after the real-life island of Hateruma) that has much more need for a doctor than for police. But one day, Shirase Ryo, a policeman gets assigned there, to the disappointment of the residents. However, as he gradually becomes friends with the people living there, he begins to help them address their own problems and concerns for the future of the island. –Tokyograph