Information about the association between cognitive functions, such as copying function, and sleep disturbances in patients with chronic obstructive pulmonary disease (COPD) is lacking. This cross-sectional observational study aimed to investigate the association between copying function and self-reported sleep quality disturbances and disease severity in an elderly COPD population. Cognitive function performances, assessed using the Mini-Mental State Examination, were compared in 562 ambulatory COPD patients with and without sleep disturbances; assessed using the Established Populations for Epidemiologic Studies of the Elderly questionnaire; and stratified by Global Initiative for Chronic Obstructive Lung Disease (GOLD) grades. Sleep disturbances overall were not correlated with cognitive functioning. A trend was revealed towards worse design copying in patients with sleep disturbances overall. GOLD I patients with difficulties falling asleep and nocturnal awakenings had worse copying ability compared to GOLD I patients without these sleep disturbances. Copying ability was worse for GOLD III than GOLD I, orientation was worse for GOLD II than GOLD I and language was worse for GOLD II and III than GOLD I. To conclude, sleep disturbances seem to be a weak correlate of cognitive functioning, and are not a marker of disease severity.