No, paper towels should not be placed in the dishwasher. Dishwashers are designed to clean and sanitize dishes, utensils, and other dishwasher-safe items, but paper towels are not meant to be washed in a dishwasher. Paper towels can break down easily when exposed to water and can cause clogs in the dishwasher's drainage system or other parts.
If you need to dispose of used paper towels, it's best to discard them in the regular trash or compost bin, depending on your local waste disposal guidelines.