The authors investigated the photoluminescence (PL) and the electron paramagnetic resonance (EPR) from an magnesium (Mg)-doped GaN thin film with a delta-doped layer. The regularly doped sample shows a PL peak at 2.776 eV for the as-grown sample, and the peak shifts to 2.904 eV and increases in intensity for the annealed sample. The delta-doped sample also shows the same PL peak as does the regularly doped sample. However, only the annealed delta-doped layer shows a sharp EPR with a small isotropic Lande g-factor, $g_{II}$, of 2.029. This resonance is attributed to the delta-doped layer, which forms a hole-bound Mg-N atomic structure instead of the $Mg_{Ga}-V_N$ defect complex, indicating that the delta-doped sample was not optically activated to form PL centers but was instead electrically activated to form a hole-bound state.