It is generally considered safe to own a pet mouse so long as you get one from a pet store. These mice will have had their required vaccinations/shots and will have been raised in sanitary conditions. It is not safe to take care of a wild mouse or one which you catch. This is because mice, like other rodents, can carry germs that can cause illness. Either way, it is imperative that you clean the cage of your mouse regularly to stop the buildup of germs, and bacteria. You will also need to clean your hands following any time that you handle them or touch items in their cage.