Cardiorespiratory Phase Synchronization (CRPS) is a manifestation of coupling between cardiac and respiratory systems complementary to Respiratory Sinus Arrhythmia. In this work, we investigated CRPS during wake and sleep stages in Polysomnographic (PSG) recordings of 30 subjects suspected from Obstructive Sleep Apnea (OSA). The population was classified into three severity groups according to the Apnea Hypopnea Index (AHI): G1 (AHI<15), G2 (15<=AHI<30) and G3 (AHI>30). The synchrogram between single lead ECG and respiratory abdominal band signals from PSG was computed with the Hilbert transform technique. The different phase locking ratios (PLR) m:n were monitored throughout the night. Ratio 4:1 was the most frequent and it became more dominant as OSA severity increased. CRPS was characterized by the percentage of synchronized time (%Sync) and the average duration of synchronized epochs (AvDurSync) using three different thresholds. Globally, we observed that %Sync significantly decreased and AvDurSync slightly increased with OSA severity. A high synchronization threshold enhanced these population differences. %Sync was significantly higher in NREM than in REM sleep in G2 and G3 groups. Population differences observed during sleep did not translate to the initial wake state. Reduced CRPS could be an early marker of OSA severity during sleep, but further studies are needed to determine whether CRPS is also present during wakefulness.