It must. Otherwise it will not be an ADU.
It also must have a bathroom. And a bedroom or two. Check your town website for the details.
But here is what the law says: “Accessory dwelling unit” means an attached or a detached residential dwelling unit that provides complete independent living facilities for one or more persons and is located on a lot with a proposed or existing primary residence. It shall include permanent provisions for living, sleeping, eating, cooking, and sanitation on the same parcel as the single-family or multifamily dwelling is or will be situated.