What's that anime movie called? (Romance, cat statue, and violin)?

It was a romance story, this girl falls in love with this boy.

The girl follows a cat and it lead her towards a store, in the store was a cat statue. (The cat was the exact one from The Cat Returns) The owners grandson was the boy. They ended up falling in love. But the boy was accepted to go to America and study the Violin for a year (or was it 3?) She has to go through those days without him. Her grades started to drop, all she cared about was finding out the same rock from the cat statue's eyes.

Then the boy came back and surprised her, in the middle of the night. Asked her to get on his bike and rode towards a secret place. There he said he knows they're still young, but when they grow up, will she marry him. She blushes and says yes. And it ends with a pretty setting.