Yes, birds sleep. Most songbirds find a secluded branch or a tree cavity, fluff out their down feathers beneath their outer feathers, turn their head to face backward and tuck their beak into their back feathers, and close their eyes.
Waterbirds sometimes sleep in the water. Some sleep on tree branches or in cavities, too. Some ducks can be literally half asleep—they close one eye and allow one half of their brain to sleep while the other eye and half of the brain is engaged in watching for predators.
Find out more, like how birds are able to stay on their perches while asleep, in this Birdsleuth article on birds and sleep.
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