In this work, we investigate the linear dynamic interactions between fluctuations in arterial CO2 that occur during normal breathing, and the BOLD fMRI signal. We cast this problem within a systems-theoretic framework, where we employ functional expansions for the estimation of the impulse responses in large regions of interest, as well as in individual voxels. We also implement classification schemes in order to identify different brain regions with similar cerebrovascular reactivity characteristics. Our results reveal that it is feasible to obtain reliable estimates of cerebrovascular reactivity curves from resting-state data and that these curves exhibit considerable variability across different brain regions that may be related to the underlying anatomy.