Because drowsiness is a major cause in vehicle accidents, its automated detection is critical. Scale-free temporal dynamics is known to be typical of physiological and body rhythms. The present work quantifies the benefits of applying a recent and original multivariate selfsimilarity analysis to several modalities of polysomnographic measurements (heart rate, blood pressure, electroencephalogram and respiration), from the MIT-BIH Polysomnographic Database, to better classify drowsiness-related sleep stages. Clinical relevance- This study shows that probing jointly temporal dynamics amongst polysomnographic measurements, with a proposed original multivariate multiscale approach, yields a gain of above 5% in the Area-under-Curve quanti-fying drowsiness-related sleep stage classification performance compared to univariate analysis.