  We combine Hubble Space Telescope spectroscopy and ground-based
integral-field data from the SAURON and OASIS instruments to study the central
black hole in the nearby elliptical galaxy NGC 3379. From these data, we obtain
kinematics of both the stars and the nuclear gaseous component. Axisymmetric
three-integral models of the stellar kinematics find a black hole of mass 1.4
(+2.6 / -1.0) x 10^8 M_sun (3 sigma errors). These models also probe the
velocity distribution in the immediate vicinity of the black hole and reveal a
nearly isotropic velocity distribution throughout the galaxy and down to the
black hole sphere of influence R_BH. The morphology of the nuclear gas disc
suggests that it is not in the equatorial plane; however the core of NGC 3379
is nearly spherical. Inclined thin-disc models of the gas find a nominal black
hole of mass 2.0 (+/- 0.1) x 10^8 M_sun (3 sigma errors), but the model is a
poor fit to the kinematics. The data are better fit by introducing a twist in
the gas kinematics (with the black hole mass assumed to be 2.0 x 10^8 M_sun),
although the constraints on the nature and shape of this perturbation are
insufficient for more detailed modelling. Given the apparent regularity of the
gas disc's appearance, the presence of such strong non-circular motion
indicates that caution must be used when measuring black hole masses with gas
dynamical methods alone.
