In this paper we propose a new method for the automatic recognition of the state of behavioral sleep (BS) and waking state (WS) in freely moving rats using their electrocorticographic (ECoG) data. Three-channels ECoG signals were recorded from frontal left, frontal right and occipital right cortical areas. We employed a simple artificial neural network (ANN), in which the mean values and standard deviations of ECoG signals from two or three channels were used as inputs for the ANN. Results of wavelet-based recognition of BS/WS in the same data were used to train the ANN and evaluate correctness of our classifier. We tested different combinations of ECoG channels for detecting BS/WS. Our results showed that the accuracy of ANN classification did not depend on ECoG-channel. For any ECoG-channel, networks were trained on one rat and applied to another rat with an accuracy of at least 80~\%. Itis important that we used a very simple network topology to achieve a relatively high accuracy of classification. Our classifier was based on a simple linear combination of input signals with some weights, and these weights could be replaced by the averaged weights of all trained ANNs without decreases in classification accuracy. In all, we introduce a new sleep recognition method that does not require additional network training. It is enough to know the coefficients and the equations suggested in this paper. The proposed method showed very fast performance and simple computations, therefore it could be used in real time experiments. It might be of high demand in preclinical studies in rodents that require vigilance control or monitoring of sleep-wake patterns.