  We present the results from a systematic search for galactic-scale, molecular
(OH 119 $\mu$m) outflows in a sample of 52 Local Volume ($d < 50$ Mpc) Burst
Alert Telescope detected active galactic nuclei (BAT AGN) with
\emph{Herschel}-PACS. We combine the results from our analysis of the BAT AGN
with the published \emph{Herschel}/PACS data of 43 nearby ($z<0.3$) galaxy
mergers, mostly ultraluminous infrared galaxies (ULIRGs) and QSOs. The objects
in our sample of BAT AGN have, on average, $\sim 10-100$ times lower AGN
luminosities, star formation rates (SFRs), and stellar masses than those of the
ULIRG and QSO sample. OH 119 $\mu$m is detected in 42 of our BAT AGN targets.
Evidence for molecular outflows (i.e. OH absorption profiles with median
velocities more blueshifted than $-$50 km s$^{-1}$ and/or blueshifted wings
with 84-percentile velocities less than $-$300 km s$^{-1}$) is seen in only
four BAT AGN (NGC~7479 is the most convincing case). Evidence for molecular
inflows (i.e. OH absorption profiles with median velocities more redshifted
than 50 km s$^{-1}$) is seen in seven objects, although an inverted P-Cygni
profile is detected unambiguously in only one object (Circinus). Our data show
that both the starburst and AGN contribute to driving OH outflows, but the
fastest OH winds require AGN with quasar-like luminosities. We also confirm
that the total absorption strength of OH 119 $\mu$m is a good proxy for dust
optical depth as it correlates strongly with the 9.7 $\mu$m silicate absorption
feature, a measure of obscuration originating in both the nuclear torus and
host galaxy disk.
