During general anesthesia, both behavioral and autonomic changes are caused by the administration of anesthetics such as propofol. Propofol produces unconsciousness by creating highly structured oscillations in brain circuits. The anesthetic also has autonomic effects due to its actions as a vasodilator and myocardial depressant. Understanding how autonomic dynamics change in relation to propofol-induced unconsciousness is an important scientific and clinical question since anesthesiologists often infer changes in level of unconsciousness from changes in autonomic dynamics. Therefore, we present a framework combining physiology-based statistical models that have been developed specifically for heart rate variability and electrodermal activity with a robust statistical tool to compare behavioral and multimodal autonomic changes before, during, and after propofol-induced unconsciousness. We tested this framework on physiological data recorded from nine healthy volunteers during computer-controlled administration of propofol. We studied how autonomic dynamics related to behavioral markers of unconsciousness: 1) overall, 2) during the transitions of loss and recovery of consciousness, and 3) before and after anesthesia as a whole. Our results show a strong relationship between behavioral state of consciousness and autonomic dynamics. All of our prediction models showed areas under the curve greater than 0.75 despite the presence of non-monotonic relationships among the variables during the transition periods. Our analysis highlighted the specific roles played by fast versus slow changes, parasympathetic vs sympathetic activity, heart rate variability vs electrodermal activity, and even pulse rate vs pulse amplitude information within electrodermal activity. Further advancement upon this work can quantify the complex and subject-specific relationship between behavioral changes and autonomic dynamics before, during, and after anesthesia. However, this work demonstrates the potential of a multimodal, physiologically-informed, statistical approach to characterize autonomic dynamics.