Multivariate time series tools may capture the nuances of the interactions between physiological systems that univariate analysis fails to characterize. This study investigates sex-specific differences in nonlinear cardiovascular coupling. The Convergent Cross-Mapping, a chaos-theory-based technique, was employed to analyze the dyadic relationship between cardiac and blood pressure dynamics. We used physiological data from the HYPOL database: RR variability (RRV), and systolic and diastolic blood pressure (SBP and DBP) time series acquired from 147 women and 129 men. Our results revealed a statistically significant causal bi-directional link between RRV and both SBP and DBP signals, which presented a higher power in the direction starting from the RRV. Furthermore, men exhibited notably stronger causal interactions between cardiovascular variables compared to women. These findings support the hypothesis of the existence of sex-related differences in multi-system physiological couplings.