This paper presents the Cardiorespiratory System Identification Lab (CRSIDLab), a MATLAB-based software tool for multivariate autonomic nervous system (ANS) evaluation through heart rate variability (HRV) analysis and cardiorespiratory system identification. Based on a graphical user interface, CRSIDLab provides a complete set of tools including pre-processing cardiorespiratory data (electrocardiogram, continuous blood pressure, airflow, and instantaneous lung volume), power spectral density estimation, and multivariable cardiorespiratory system model identification. Parametrized multivariate models can assess both HRV and baroreflex sensitivity (BRS) by considering the causal relationship from respiration to heart rate (or its reciprocal, R-to-R interval - RRI) and from systolic blood pressure to RRI, for instance. The impulse response, estimated from the model, is used as a mathematical tool to effectively open the inherently closed-loop nature of the cardiorespiratory system, allowing the investigation of the dynamic response between pairs of cardiorespiratory variables. This system modeling approach provides information on gain and temporal behavior regarding dynamics, such as the baroreflex, complementing traditional HRV, and BRS indices. The toolbox is presented and used to investigate autonomic function in sleep apnea. The results show that, while traditional HRV indices were unable to differentiate between apneic and non-apneic subjects, the autonomic descriptors obtained from the multivariate system identification techniques were able to show vagal impairment in apneic compared to non-apneic subjects. Thus, CRSIDLab can help promote the use of cardiorespiratory system identification as a potentially more sensitive measure of ANS activity than classical HRV analysis.