You and Me.

 Kimi to Boku (You and I) is the story of an aspiring mangaka and his cat, told from the cat's perspective. It follows the friendship between the cat and the young man from when they first meet up to when they must part.

Note: The first version was released to the public in 2001, since then there have been version upgrades, possibly with additional animation or simply improved quality. The English version also contains a prologue about the history of the Tanabata festival, making it much longer.

(Source: AniDB)