Past research efforts aiming at obtaining stable p-type ZnO have been based on complexes involving nitrogen doping. A recent experiment by (J. G. Reynolds et al., Appl. Phys. Lett., 2013, 102, 152114) demonstrated a significant (∼10¹⁸ cm⁻³) p-type behavior in N-doped ZnO films after appropriate annealing. The p-type conductivity was attributed to a V_Zn–N_O–H shallow acceptor complex, formed by a Zn vacancy (V_Zn), N substituting O (N_O), and H interstitial (H_i). We present here a first-principles hybrid functional study of this complex compared to the one without hydrogen. Our results confirm that the V_Zn–N_O–H complex acts as an acceptor in ZnO. We find that H plays an important role, because it lowers the formation energy of the complex with respect to V_Zn–N_O, a complex known to exhibit (unstable) p-type behavior. However, this additional H atom also occupies the hole level at the origin of the shallow behavior of V_Zn–N_O, leaving only two states empty higher in the band gap and making the V_Zn–N_O–H complex a deep acceptor. Therefore, we conclude that the cause of the observed p-type conductivity in experiment is not the presence of the V_Zn–N_O–H complex, but probably the formation of the V_Zn–N_O complex during the annealing process.