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Service animals are generally permitted to accompany their disabled owners any place where the general public are permitted to go, including hotels and motels. Lodging establishments are not permitted to charge extra for the service animal or to require a deposit. However, the owner of the service animal would still be responsible for any damages done to the facilities.
A representative of the hotel or motel is permitted to inquire as to what the dog is trained to do to mitigate the owner's disability. If the dog is not trained to perform specific tasks, then it is not a service dog and they are not required to permit it.