  The stellar and gaseous mass distributions, as well as the extended rotation
curve in the nearby galaxy M33 are used to derive the radial distribution of
dark matter density in the halo and to test cosmological models of galaxy
formation and evolution. Two methods are examined to constrain dark mass
density profiles. The first method deals directly with fitting the rotation
curve data in the range of galactocentric distances $0.24\,\text{kpc}\leq
r\leq22.72\,\text{kpc}.$ As found in a previous paper by
\citet{Corbelli:2014lga}, and using the results of collisionless $\Lambda-$Cold
Dark Matter numerical simulations, we confirm that the Navarro-Frenkel-White
(hereafter NFW) dark matter profile provides a better fit to the rotation curve
data than the cored Burkert profile (hereafter BRK) profile. The second method
relies on the local equation of centrifugal equilibrium and on the rotation
curve slope. In the aforementioned range of distances we fit the observed
velocity profile, using a function which has a rational dependence on the
radius, and derive the slope of the rotation curve. Following
\citet{Salucci:2010qr} we then infer the effective matter densities. In the
radial range $9.53\,\text{kpc}\leq r\leq22.72\,\text{kpc}$ the uncertainties
induced by the luminous matter (stars and gas) becomes negligible, because the
dark matter density dominates, and we can determine locally the radial
distribution of dark matter. With this second method we tested the NFW and the
BRK dark matter profiles and confirm that both profiles are compatible with the
data even though in this case the cored BRK density profile provides a more
reasonable value for the baryonic-to-dark matter ratio.
