An increasing problem in today's society is the spiraling number of people suffering from various sleep disorders. The research results presented in this paper support the use of a novel method that employs techniques from the classification of sleep disorders for more accurate scoring. Applying this novel method will assist researchers with better analyzing subject profiles for recommending prescriptions or to alleviate sleep disorders. In biomedical research, the use of animal models is required to experimentally test the safety and efficacy of a drug in the pre-clinical stage. We have developed a novel LSTM Recurrent Neural Network to process Pharmaco-EEG Profiles of rats to automatically score their sleep-wake stages. The results indicate improvements over the current methods; for the case of combined channels, the model accuracy improved by 1% and 3% in binary or multiclass classifications, respectively, to accuracies of 93% and 82%. In the case of using a single channel, binary and multiclass LSTM models for identifying rodent sleep stages using single or multiple electrode positions for binary or multiclass problems have not been evaluated in prior literature. The results reveal that single or combined channels, and binary or multiclass classification tasks, can be applied in the automatic sleep scoring of rodents.