From the Super Mario Wiki
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“STAR Bunny, STAR Festival! Yes, I'm sensing a connection here.”
Star Bunnies are a type of Rabbit found in the Wii games, Super Mario Galaxy and Super Mario Galaxy 2. Many, but not all, Star Bunnies are actually Lumas which have transformed into Star Bunnies. As seen when they are first encountered, the transformation is two-way and reversible. Star Bunnies appear throughout the galaxies and they most often need to be caught in a game of hide-and-seek. They usually end their sentences with "boiyoing".
Star Bunnies are small white rabbits with long teeth and whiskers. Their fur is completely white except for at the very top of the bunny's ears where there is one yellow star-shaped tip to both of the Star Bunny's ears. Its feet are bigger than its other body parts and its tail is also yellow. In both Super Mario Galaxy and Super Mario Galaxy 2, some Star Bunnies wear vests (in the latter game, they usually wear Toad vests). A few of them have blue star-shaped tips on their ears instead of bright yellow.
Super Mario Galaxy
Some Star Bunnies appear in Super Mario Galaxy. They appear in many levels as playful rabbits with the ability to speak and they try to get Mario to play hide and seek with them. The Star Bunnies will hide and Mario (or Luigi) will have to find them and then corner them. They appear in the very first level of the game and then in many levels thereafter as obstacles. In some levels the bunnies do not appear as obstacles but instead as aids for Mario as they give him tips on what to do in the level that he is in. If Mario catches one of the bunnies that play hide and seek, Mario will get a Power Star. In this game their home seems to be the Gusty Garden Galaxy.
Super Mario Galaxy 2
They appear again in Super Mario Galaxy 2. They are first encountered in the Flip-Swap Galaxy where a blue Star Bunny teaches Mario how to traverse the galaxy's obstacles. They later appear in larger numbers in the Freezy Flake Galaxy where some local Star Bunnies are frightened of the numerous snow-sculptures in the shape of Bowser and his Goombas that have been appearing all over their galaxy. Star Bunnies are also one of the many species that will be found on Starship Mario after completing the Think Before You Shake mission in the Flip-Swap Galaxy. In the Cosmic Cove Galaxy, Mario must catch a Star Bunny which will give him a Power Star after he is caught like in the first game.