The electronic and magnetic structures of tetragonal, Cu2Sb-type CrMnAs were examined using density functional theory. To obtain reasonable agreement with reported atomic and low-temperature magnetic ordering in this compound, the intra-atomic electron-electron correlation in term of Hubbard U on Mn atoms are necessary. Using GGA+U, calculations identify four low-energy antiferromagnetically ordered structures, all of which adopt a magnetic unit cell that contains the same direct CrCr and CrMn magnetic interaction, as well as the same indirect MnMn magnetic interaction across the Cr planes. One of these low-energy configurations corresponds to the reported case. Effective exchange parameters for metal-metal contacts obtained from SPRKKR calculations indicate both direct and indirect exchange couplings play important roles in tetragonal CrMnAs.