Introduction: Overlap syndrome (OS) is defined by the combined occurrence of obstructive sleep apnea (OSA) and chronic obstructive pulmonary disease (COPD). Sleep-related breathing disorders (SRBDs) in OS can also manifest with central sleep apnea (CSA) and hypoventilation; besides OSA. Methods: This study was carried out to evaluate various SRBD in OS and its therapeutic implications patients having postbronchodilator obstruction in spirometry with respiratory symptoms were classified as COPD. Those found to have an apnea–hypopnea Index (AHI) >5/h in polysomnography (PSG) were diagnosed as OS. All 37 patients diagnosed as OS underwent a subsequent positive airway pressure (PAP) titration. Results: On the evaluation of the SRBD, over half (51%) of the patients had OSA with no hypoventilation. More than one-third of the patients (35%) had associated hypoventilation with OSA, three patients had hypercapnic CSA, and two patients had hypocapnic CSA with Cheyne–Stokes breathing (CSA-CSB). The OSA group was easily titrated and corrected by CPAP therapy. OSA with hypoventilation group had underlying COPD with severe obstruction requiring bilevel PAP titration. Patients with CSA-CSB were elderly hypertensive patients with congestive heart failure who were corrected by PAP and optimization of cardiac medications. Patients with hypoventilation and hypercapnic CSA were most difficult to titrate and needed a backup rate along with PAP therapy for correction. On classifying patients on the basis of severity of OSA and COPD, there was no correlation found between AHI and forced expiratory volume 1 (FEV1). Patients with mild COPD with severe OSA were easily titrated with CPAP with a mean pressure of 8 cm H2 0. The most challenging cases were with severe COPD with severe OSA who required high pressures in both exhalation PAP and inspiratory PAP titration; two of such patients required backup rate by spontaneous/timed mode of PAP therapy. Conclusions: There are many profiles of SRBD in OS, and a detailed in-hospital PSG with a PAP titration can help in effectively managing the patients.