According to the Washington Department of Fish and Wildlife, possums, or opossums, do not sleep upside down, hanging from their tails. They are nocturnal animals that sleep during the day in dens, hollow stumps and logs or other hidden sites.
The WDFW indicates that possums do use their tails for many activities. They wrap their tails around grasses and leaves and then take the materials to their sleeping areas to build warm nests. A mother possum carries her babies on her back, and the young use their feet and tails to cling to her. In addition, when possums climb trees in search of escape, food or a resting spot, they wrap their tails around branches for support.