  We present high spatial resolution, integral field spectrograph (IFS)
observations of the nearby LINER (low ionization nuclear emission line region)
galaxy NGC 404 at 1.25 $\mu$m (J band) and 2.2 $\mu$m (K band) near-infrared
wavelengths. Although NGC 404 is thought to host an intermediate mass black
hole at its center, it has been unclear whether accretion onto the black hole
or another mechanism such as shock excitation drives its LINER emission at
optical/near-infrared wavelengths. We use the OSIRIS IFS at Keck Observatory
behind laser guide star adaptive optics to map the strength and kinematics of
[FeII], H$_2$, and hydrogen recombination lines at spatial resolutions of 1 pc
across the central 30 pc of the galaxy. The H$_2$ gas is in a central rotating
disk and ratios of multiple H$_2$ lines indicate that the molecular gas is
thermally excited, with some contribution from UV fluorescence. The [FeII]
emission is more extended and diffuse than the molecular gas and has a
different kinematic structure that reaches higher velocities/dispersions. We
also map the strength of the CO stellar absorption feature and constrain the
dominant age of the nuclear stellar population to $\sim$1 Gyr. Finally, we find
regions across the nucleus of NGC 404 with [FeII]/Pa$\beta$ line ratios up to
6.5, $\sim$2.5 times higher than the ratio measured from spatially-integrated
spectra. From these high line ratios, we conclude that shocks are the dominate
physical mechanism exciting NGC 404's LINER emission and argue that a possible
source of this shock excitation is a supernova remnant.
