  We have obtained two-dimensional velocity fields of the dwarf spiral galaxy
NGC 2976 in Halpha and CO. The high spatial (~75 pc) and spectral (13 km/s and
2 km/s, respectively) resolution of these observations, along with our
multicolor optical and near-infrared imaging, allow us to measure the shape of
the density profile of the dark matter halo with good precision. We find that
the total (baryonic plus dark matter) mass distribution of NGC 2976 follows a
rho_tot ~ r^(-0.27 +/- 0.09) power law out to a radius of 1.8 kpc, assuming
that the observed radial motions provide no support. The density profile
attributed to the dark halo is even shallower, consistent with a nearly
constant density of dark matter over the entire observed region. A maximal disk
fit yields an upper limit to the K-band stellar mass-to-light ratio (M*/L_K) of
0.09^{+0.15}_{-0.08} M_sun/L_sun,K (including systematic uncertainties), with
the caveat that for M*/L_K > 0.19 M_sun/L_sun,K the dark matter density
increases with radius, which is unphysical. Assuming 0.10 M_sun/L_sun,K <
M*/L_K < 0.19 M_sun/L_sun,K, the dark matter density profile lies between
rho_dm ~ r^-0.17 and rho_dm ~ r^-0.01. Therefore, independent of any
assumptions about the stellar disk or the functional form of the density
profile, NGC 2976 does not contain a cuspy dark matter halo. We also
investigate some of the systematic effects that can hamper rotation curve
studies, and show that 1) longslit rotation curves are far more vulnerable to
systematic errors than two-dimensional velocity fields, 2) NGC 2976 contains
large radial motions at small radii, and 3) the Halpha and CO velocity fields
of NGC 2976 agree within their uncertainties. [slightly abridged]
