Obstructive Sleep Apnea (OSA) is a serious sleep disorder where patient experiences frequent upper airway collapse leading to breathing obstructions and arousals. Severity of OSA is assessed by averaging the number of incidences throughout the sleep. In a routine OSA diagnosis test, overnight sleep is broadly categorized into rapid eye movement (REM) and non-REM (NREM) stages and the number of events are considered accordingly to calculate the severity. A typical respiratory event is mostly accompanied by sounds such as loud breathing or snoring interrupted by choking, gasps for air. However, respiratory controls and ventilations are known to differ with sleep states. In this study, we assumed that the effect of sleep on respiration will alter characteristics of respiratory sounds as well as snoring in OSA patients. Our objective is to investigate whether the characteristics are sufficient to label snores of REM and NREM sleep. For investigation, we collected overnight audio recording from 12 patients undergoing routine OSA diagnostic test. We derived features from snoring sounds and its surrounding audio signal. We computed time series statistics such as mean, variance, inter-quartile-range to capture distinctive pattern from REM and NREM snores. We designed a Naïve Bayes classifier to explore the usability of patterns to predict corresponding sleep states. Our method achieved a sensitivity of 92% (±9%) and specificity of 81% (±9%) in labeling snores into REM/NREM group which indicates the potential of snoring sounds to differentiate sleep states. This may be valuable to develop non-contact snore based technology for OSA diagnosis