Josee, the Tiger and the Fish

Tsuneo is an ordinary college student taking his boss's dog out for a walk one day when out of nowhere a large baby carriage barrels down a hill and bumps into a nearby guardrail. After a brief confused pause he decides to check the carriage for passengers. Instead of a baby he sees Josee, a girl about his age who suffers from cerebral palsy and has spent her entire life insulated from the outside world by her eccentric overprotective grandmother. Although the two have nothing in common and don't get along at first, Josee's quirky personality intrigues Tsuneo and the two end up spending much more time together.
(Source: Eiga Wiki)
~~ Adapted from the short story "Josee, the Tiger and the Fish" (ジョゼと虎と魚たち) by Tanabe Seiko (田辺聖子).