Background: Multiple clinical departments are involved in the provision of obstructive sleep apnoea (OSA) therapy in Japan. Inconsistent results regarding the association between depression and OSA have been reported. Methods: This cross-sectional survey compared newly diagnosed OSA patients at two outpatient sleep apnoea units in Shiga Prefecture, Japan: one associated with the psychiatry department (n = 583), and the other with the otolaryngology department (n = 450). Results: The unit associated with the psychiatry department had more patients referred by psychiatrists than that with the otolaryngology department (11% vs. 3% p < 0.05). Sleepiness, insomnia, and depression were assessed using the Epworth Sleepiness Scale (ESS), Athens Insomnia Scale (AIS), and Patient Health Questionnaire-9 (PHQ-9), respectively. The ESS, AIS, and PHQ-9 scores were higher in the sleep unit in the psychiatry department (p < 0.001 each). Snoring and moderate to severe OSA were more prevalent in the unit attached to the otolaryngology department (p < 0.001 each). Patients with moderate to severe OSA had lower PHQ-9 scores than those with no to mild OSA (OR: 0.96, 95% CI: 0.92–1.00, p = 0.042). Conclusion: Patients with sleepiness, insomnia, and depressive symptoms were more likely to attend a sleep outpatient unit associated with a psychiatry department, whereas those with snoring and sleep apnoea attended that associated with an otolaryngology department. OSA severity was negatively associated with depressive symptoms.