Bats do live in trees.
Many species of bats roost in trees. Those that prefer sunlight will roost directly on branches while others will nest inside of a hollow tree or slip beneath the bark to roost. Roosting requirements vary between species and also vary with seasonal and mating needs. Bats choose their roosts depending on their feeding habits and environmental needs, which include light, temperature, and humidity. You will find bats in caves, buildings, trees, under leaves, on the surface of rocks...anywhere that meets the needs of the bat species providing them with shelter from predators and bad weather.
The little brown bat is an example of a species that roosts in trees during a particular season. During the winter months, the little brown bat will hibernate in mines or caves. During the warmer months, the females will roost in nursery colonies in trees or buildings.