  We have analyzed ROSAT PSPC X-ray data of the optically elongated S0 galaxy
NGC 1332 with the purposes of constraining the intrinsic shape of its
underlying mass and presenting a detailed investigation of the uncertainties
resulting from the assumptions underlying this type of analysis. The X-ray
isophotes are elongated with ellipticity $0.10 - 0.27$ (90% confidence) for
semi-major axes $75\arcsec -90\arcsec$ and have orientations consistent with
the optical isophotes (ellipticity $\sim 0.43$). The spectrum is poorly
constrained by the PSPC data and cannot rule out sizeable radial temperature
gradients or an emission component due to discrete sources equal in magnitude
to the hot gas. Using (and clarifying) the "geometric test" for dark matter, we
determined that the hypothesis that mass-traces-light is not consistent with
the X-ray data at 68% confidence and marginally consistent at 90% confidence
independent of the gas temperature profile. Detailed modeling gives constraints
on the ellipticity of the underlying mass of \epsilon_{mass} = 0.47 - 0.72
(0.31 - 0.83) at 68% (90%) confidence for isothermal and polytropic models. The
total mass of the isothermal models within a=43.6$ kpc (D = 20h^{-1}_{80} Mpc)
is M_{tot} = (0.38 - 1.7) \times 10^{12}M_{\sun} (90% confidence) corresponding
to total blue mass-to-light ratio \Upsilon_B = (31.9 - 143) \Upsilon_{\sun}.
Similar results are obtained when the dark matter is fit directly using the
known distributions of the stars and gas. When possible rotation of the gas and
emission from discrete sources are included flattened mass distributions are
still required, although the constraints on $\epsilon_{mass}$, but not the
total mass, are substantially weakened.
