Most cats enjoy being petted while they are sleeping. The rhythmic strokes of your hand can help them relax and feel comfortable. Some cats may even start to purr when they are being petted. However, there are a few things to keep in mind when petting a sleeping cat. First, let the cat initiate the interaction. If the cat moves away or seems uncomfortable, stop petting them. Secondly, be sure to stroke the cat in the direction that their fur lies. This will help prevent them from feeling agitated or uncomfortable. Finally, avoid waking a sleeping cat if possible. They may not be as receptive to being handled if they are half-asleep!