  The Local Group galaxy M33 exhibits a regular spiral structure and is close
enough to permit high resolution analysis of its kinematics, making it an ideal
candidate for rotation curve studies of its inner regions. Previous studies
have claimed the galaxy has a dark matter halo with an NFW profile, based on
statistical comparisons with a small number of other profiles. We apply a
Bayesian method from our previous paper to place the dark matter density
profile in the context of a continuous, and more general, parameter space. For
a wide range of initial assumptions we find that models with inner log slope
$\gamma_{\rm in}<0.9$ are strongly excluded by the kinematics of the galaxy
unless the mass-to-light ratio of the stellar components in the $3.6\mu$m band
satisfies $\Upsilon_{3.6}\geq2$. Such a high $\Upsilon_{3.6}$ is inconsistent
with current modelling of the stellar population of M33. This suggests that M33
is a galaxy whose dark matter halo has not been significantly modified by
feedback. We discuss possible explanations of this result, including ram
pressure stripping during earlier interactions with M31.
