Yes. The ceramic-coated basket, the crisper plate, and any accessories are dishwasher safe.
If that didn't work: For stuck-on food, place the basket and crisper plate in a sink filled with warm, soapy water to soak first.
Heads up: Never clean the main unit in the dishwasher. Never immerse the main unit in water. Wipe it with a damp cloth only.