2026ApJS..282...68G

We present an analysis of near-infrared (NIR) emission-line properties, active galactic nucleus (AGN) diagnostics, and circumnuclear gas dynamics for 453 hard X-ray selected (14-195 keV) AGNs from the BAT AGN Spectroscopic Survey NIR Data Release 3 (DR3; 〈z〉 = 0.036, z < 1.0). This dataset is the largest compilation of rest-frame NIR spectroscopic observations of hard-X-ray-selected AGNs and includes the full DR2 sample. Observations were obtained with the Very Large Telescope X-Shooter, a multiwavelength (0.3-2.5 μm) spectrograph (R = 4000-18,000), using a ≥ 2σ detection threshold, enabling broad analysis of emission features. We find that NIR coronal lines, particularly [Si VI] λ1.964, are more reliable tracers of AGN luminosity than optical $\left[{\rm{O}}\,{\rm\small{III}}\right]$, showing a tighter correlation with hard X-ray luminosity (σ = 0.25 dex) than $\left[{\rm{O}}\,{\rm\small{III}}\right]$λ5007 (σ = 0.55 dex). Broad Paschen lines (Paα and Paβ) are detected in 12% of Seyfert 2 and 57% of Seyfert 1.9 galaxies, consistent with previous hidden broad-line region (BLR) studies. We introduce a refined NIR diagnostic diagram ([Fe II] λ1.257 μm/Paβ and H₂λ2.122 μm/Brγ) that effectively distinguishes AGN, star-forming, and composite sources even when contamination limits individual diagnostics or only upper limits are available. Additionally, we find a moderate correlation (p ≈ 7.4 × 10^–3) between hot molecular gas mass (traced by H₂ 2.121 μm) and X-ray luminosity, while its relation with Eddington ratio is weaker. The hot-to-cold gas mass ratio spans 4 orders of magnitude, averaging ∼3 × 10^–7, indicating diverse molecular gas excitation processes likely driven by star formation and AGN feedback. Our results underscore the value of NIR spectroscopy in probing AGN activity, obscured BLRs, and the complex interactions between AGNs and their circumnuclear environments.