  We present the BAT AGN Spectroscopic Survey (BASS) Near-infrared Data Release
2 (DR2), a study of 168 nearby ($\bar z$ = 0.04, $z$ < 0.6) active galactic
nuclei (AGN) from the all-sky Swift Burst Array Telescope X-ray survey observed
with Very Large Telescope (VLT)/X-shooter in the near-infrared (NIR; 0.8 - 2.4
$\mu$m). We find that 49/109 (45%) Seyfert 2 and 35/58 (60%) Seyfert 1 galaxies
observed with VLT/X-shooter show at least one NIR high-ionization coronal line
(CL, ionization potential $\chi$ > 100 eV). Comparing the emission of the [Si
vi] $\lambda$1.9640 CL with the X-ray emission for the DR2 AGN, we find a
significantly tighter correlation, with a lower scatter (0.37 dex) than for the
optical [O iii] $\lambda$5007 line (0.71 dex). We do not find any correlation
between CL emission and the X-ray photon index $\Gamma$. We find a clear trend
of line blueshifts with increasing ionization potential in several CLs, such as
[Si vi] $\lambda$1.9640, [Si x] $\lambda$1.4300, [S viii] $\lambda$0.9915, and
[S ix] $\lambda$1.2520, indicating the radial structure of the CL region.
Finally, we find a strong underestimation bias in black hole mass measurements
of Sy 1.9 using broad H$\alpha$ due to the presence of significant dust
obscuration. In contrast, the broad Pa$\alpha$ and Pa$\beta$ emission lines are
in agreement with the $M$-$\sigma$ relation. Based on the combined DR1 and DR2
X-shooter sample, the NIR BASS sample now comprises 266 AGN with rest-frame NIR
spectroscopic observations, the largest set assembled to date.
