  In this study, we use the SWIFT/BAT AGN sample, which has received extensive
multiwavelength follow-up analysis as a result of the BAT AGN Spectroscopic
Survey (BASS), to develop a diagnostic for nuclear obscuration by examining the
relationship between the line-of-sight column densities ($N_{\rm{H}}$), the
2-10 keV-to-$12\,\rm{\mu m}$ luminosity ratio, and WISE mid-infrared colors. We
demonstrate that heavily obscured AGNs tend to exhibit both preferentially
''redder'' mid-infrared colors and lower values of
$L_{\rm{X,\,Obs.}}$/$L_{12\,\rm{\mu m}}$ than less obscured AGNs, and we derive
expressions relating $N_{\rm{H}}$ to the $L_{\rm{X,\,Obs.}}$/$L_{12\,\rm{\mu
m}}$ and $L_{22\,\rm{\mu m}}$/$L_{4.6\,\rm{\mu m}}$ luminosity ratios as well
as develop diagnostic criteria using these ratios. Our diagnostic regions yield
samples that are $\gtrsim80$% complete and $\gtrsim60$% pure for AGNs with
log($N_{\rm{H}})\geq24$, as well as $\gtrsim85$% pure for AGNs with
$\rm{log}(N_{\rm{H}})\gtrsim23.5$. We find that these diagnostics cannot be
used to differentiate between optically star forming galaxies and active
galaxies. Further, mid-IR contributions from host galaxies that dominate the
observed $12~\rm{\mu m}$ emission can lead to larger apparent X-ray deficits
and redder mid-IR colors than the AGNs would intrinsically exhibit, though this
effect helps to better separate less obscured and more obscured AGNs. Finally,
we test our diagnostics on two catalogs of AGNs and infrared galaxies,
including the XMM-Newton XXL-N field, and we identify several known
Compton-thick AGNs as well as a handful of candidate heavily obscured AGNs
based upon our proposed obscuration diagnostics.
