  We measure the central kinematics for the dwarf spheroidal galaxy Leo I using
integrated-light measurements and previously published data. We find a steady
rise in the velocity dispersion from $300^{\prime\prime}$ into the center. The
integrated-light kinematics provide a velocity dispersion of $11.76\pm0.66$
km/s inside $75^{\prime\prime}$. After applying appropriate corrections to
crowding in the central regions, we achieve consistent velocity dispersion
values using velocities from individual stars. Crowding corrections need to be
applied when targeting individual stars in high density stellar environments.
From integrated light, we measure the surface brightness profile and find a
shallow cusp towards the center. Axisymmetric, orbit-based models measure the
stellar mass-to-light ratio, black hole mass and parameters for a dark matter
halo. At large radii it is important to consider possible tidal effects from
the Milky Way so we include a variety of assumptions regarding the tidal
radius. For every set of assumptions, models require a central black hole
consistent with a mass $(3.3 \pm 2) \times 10^6\, M_\odot$. The no-black-hole
case for any of our assumptions is excluded at over 95% significance, with
$6.4<\Delta\chi^2<14$. A black hole of this mass would have significant effect
on dwarf galaxy formation and evolution. The dark halo parameters are heavily
affected by the assumptions for the tidal radii, with the circular velocity
only constrained to be above 30 km/s. Reasonable assumptions for the tidal
radius result in stellar orbits consistent with an isotropic distribution in
the velocities. These more realistic models only show strong constraints for
the mass of the central black hole.
