Cobalt based perovskites have great potential for numerous applications. Contrary to a generally assumed hexagonal space group (SG P63/mmc) model as the ground state of BaCoO3 (BCO), our hybrid DFT calculations with B1WC density functional and the symmetry group-subgroup derived crystal structure model support the ground state of BCO to be indeed monoclinic, in agreement with recent experimental predictions [Chin et al., Phys. Rev. B, 2019, 100, 205139]. We found for the monoclinic BCO that the C-type anti-ferromagnetic low-spin (AFM LS) state (SG P2/c) is energetically only slightly more preferential at 0 K than the ferromagnetic (FM) LS state (SG C2/c). In turn, these monoclinic structures are energetically more favourable than the hexagonal ones, due to slight z-axis tilting. The analysis of density of states (DOS) and crystal orbital overlap population (COOP) shows a significant (almost 2 eV) separation between occupied and empty t2g states (in the spin-down channel and corresponding anti-bonding states) induced by the z-axis tilting.