  We study the interplay between electronic correlations and hybridization in
the low-energy electronic structure of CaMn$_2$Bi$_2$, a candidate
hybridization-gap semiconductor. Utilizing a DFT+$U$ approach we find both the
antiferromagnetic N\'eel order and band gap in good agreement with the
corresponding experimental values. We further find that, under hydrostatic
pressure, the band gap is mainly governed by magnetic correlations, whereas
hybridization has a greater impact on states at higher band energies. This
result suggests that CaMn$_2$Bi$_2$ is more closely related to the
high-temperature superconducting cuprates and iron pnictides than the heavy
fermion class of materials. Finally, we also find the antiferromagnetic
CaMn$_2$Bi$_2$ to be topologically trivial for all pressures studied.
