This paper presents a new and robust algorithm for detection of sleep stages by using the lead I of the Electrocardiography (ECG) and a fingertip Photoplethysmography (PPG) sensor, validated using multiple overnight PSG recordings consisting of 20 human subjects (9 insomniac and 11 healthy). Heart Rate Variability (HRV) and Pulse Transit Time (PTT) biomarkers which were extracted from ECG and PPG biosignals then employed to extract features. Distance Weighted k-Nearest Neighbours (DWk-NN) was used as classifier to differentiate sleep epochs. The validation of the algorithm was evaluated by Leave-One-Out-Cross-Validation method. The average accuracy of 73.4% with standard deviation of 6.4 was achieved while the algorithm could distinguish stages 2, 3 of non-rapid eye movement sleep by average sensitivity of almost 80%. The lowest mean sensitivity of 53% was for stage 1. These results demonstrate that an algorithm based on PTT and HRV spectral analysis is able to classify and distinguish sleep stages with high accuracy and sensitivity. In addition the proposed algorithm is capable to be improved and implemented as a wearable, comfortable and cheap instrument for sleep screening.