  We examine the 0.1 to 10.0 keV X-ray spectrum of the bright nuclear LINER
galaxy NGC 1052, one of two elliptical galaxies known to contain a luminous H2O
maser. The observed 2.0-10.0 keV spectrum is unusually flat (photon index
Gamma~0.2) and best described as intrinsically power-law shaped nuclear flux
that is either (1) attenuated by a complex absorber with ~70% of the nuclear
flux absorbed by a column density of NH ~ 3x10^23 cm^{-2} and ~30% absorbed by
a column density of NH ~ 3-5x10^{22} cm^{-2}, or (2) reprocessed, with the
nuclear source blocked and the X-rays Compton reflected in our direction by
high column density (>=10^{24} cm^{-2}) gas. The moderate equivalent width of
the Fe K-alpha line favors the dual absorption model as the most likely
scenario. The 0.1-2.0 keV spectrum does not resemble the few times 10^6 to 10^7
K thermal emission typically found in other elliptical galaxies, but instead is
best described as nuclear X-rays leaking through a patchy absorber or scattered
in our direction by low-density, ionized gas with the thermal contribution
limited to about 15% for solar abundances. The absorption-corrected 2-10 keV
luminosity of the nuclear source is L_X ~ 8x10^{41} ergs s^{-1} or L_X ~
2x10^{43} ergs s^{-1} for the dual-absorption and Compton-reflection models,
respectively. The absorbing and H2O masing gases appear to be spatially
separate in this galaxy.
