Polysomnography (PSG) remains the gold standard for sleep monitoring but is obtrusive in nature. Advances in camera sensor technology and data analysis techniques enable contactless monitoring of heart rate variability (HRV). In turn, this may allow remote assessment of sleep stages, as different HRV metrics indirectly reflect the expression of sleep stages. We evaluated a camera-based remote photoplethysmography (PPG) setup to perform automated classification of sleep stages in near darkness. Based on the contactless measurement of pulse rate variability, we use a previously developed HRV-based algorithm for 3 and 4-class sleep stage classification. Performance was evaluated on data of 46 healthy participants obtained from simultaneous overnight recording of PSG and camera-based remote PPG. To validate the results and for benchmarking purposes, the same algorithm was used to classify sleep stages based on the corresponding ECG data. Compared to manually scored PSG, the remote PPG-based algorithm achieved moderate agreement on both 3 class (Wake-N1/N2/N3-REM) and 4 class (Wake-N1/N2-N3-REM) classification, with average kappa of 0.58 and 0.49 and accuracy of 81% and 68%, respectively. This is in range with other performance metrics reported on sensing technologies for wearable sleep staging, showing the potential of video-based non-contact sleep staging.