Despite their striking resemblance (minus the wings of course), bats are not closely related to mice. In fact, the two are not related at all. Although bats and mice are both mammals, bats belong to the mammalian order Chiroptera, while rodents are of the mammalian order Rodentia.
It is not certain where confusion comes into play when it comes to people thinking that these two creatures might be related. It could be because they look somewhat similar, or it could also be because in many languages the word for “bat” is cognate with the word for “mouse”. In some countries/languages, bats are often referred to as the “winged mouse”, “winged rodent”, “blind mouse”, or “leather mouse”. It is no wonder that people are so confused.