Despite sleep disturbances are common among youths with Down syndrome (DS), the cognitive and behavioral features associated with sleep problems have not yet been studied extensively. The present study investigated the presence of sleep disturbances in a group of children and adolescents with DS and their cognitive and behavioral correlates. Seventy-one children and adolescents with DS underwent a neuropsychological evaluation, whereas parents completed questionnaires for the screening of the child’s sleep, emotional and behavioral problems. We found no association between sleep disturbances and sex, nonverbal IQ, nor adaptive abilities. However, we found that age was positively associated with disorders in initiating and maintaining sleep (DIMS) and disorders of excessive somnolence (DOES), while body mass index was related with DOES. We also detected a relationship between visual-motor integrations and DIMS, as well as multiple associations between sleep disturbances and psychopathological and behavioral problems, mainly externalizing symptoms. The present study provided a detailed characterization of sleep problems in relation to several features of youths with DS. The proper identification of sleep disturbances profile in the DS population could support the process of clinical evaluation, in particular for psychopathological aspects.