Analysis of brain connectivity is important for understanding how information is processed by the brain. We propose a novel Bayesian vector autoregression (VAR) hierarchical model for analyzing brain connectivity in a resting-state fMRI data set with autism spectrum disorder (ASD) patients and healthy controls. Our approach models functional and effective connectivity simultaneously, which is new in the VAR literature for brain connectivity, and allows for both group- and single-subject inference as well as group comparisons. We combine analytical marginalization with Hamiltonian Monte Carlo (HMC) to obtain highly efficient posterior sampling. The results from more simplified covariance settings are, in general, overly optimistic about functional connectivity between regions compared to our results. In addition, our modeling of heterogeneous subject-specific covariance matrices is shown to give smaller differences in effective connectivity compared to models with a common covariance matrix to all subjects.