Technically they don’t sleep nor do they need to sleep since they’re dead. However a zombie hoard will stop after a certain amount of time with their heads hanging down while remaining motionless if no prey is present. Zombies that wander off alone will eventually collapse, and appear truly dead if no prey or other zombies are seen after a period of time. However they’ll pop back up again the minute they smell or hear any humans, animals, or zombies. Sometimes weather conditions including a brisk wind will get them animated again. Never assume that a motionless zombie lying on the ground is harmless. Destroy the brain, and ask questions later!
On a related note I’m half zombie, and I only sleep 3-4 hours a night. Clearly that’s all my human half needs despite the average adult requiring 7-8 hours of sleep per night.