Overnight polysomnography (PSG) is the gold standard tool used to characterize sleep and for diagnosing sleep disorders. PSG is a non-invasive procedure that collects various physiological data which is then scored by sleep specialists who assign a sleep stage to every 30-second window of the data according to predefined scoring rules. In this study, we aimed to automate the process of sleep stage scoring of overnight PSG data while adhering to expert-based rules. We developed an algorithm utilizing a likelihood ratio decision tree classifier and extracted features from EEG, EMG and EOG signals based on predefined rules of the American Academy of Sleep Medicine Manual. Specifically, features were computed in 30-second epochs in the time and the frequency domains of the signals and used as inputs to the classifier which assigned each epoch to one of five possible stages: N3, N2, N1, REM or Wake. The algorithm was trained and tested on PSG data from 38 healthy individuals with no reported sleep disturbances. The overall scoring accuracy was 80.70% on the test set, which was comparable to the training set. Our results imply that the automatic classification is highly robust, fast, consistent with visual scoring and is highly interpretable.