We examine the 0.1-10.0 keV X-ray spectrum of the bright nuclear LINER gala
xy 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 similar to 0.2) and is best described as intrinsically power-law shap
ed nuclear flux that is either (1) attenuated by a complex absorber with si
milar to 70% of the nuclear flux absorbed by a column density of N-H simila
r to 3 x 10(23) cm(-2) and similar to 30% absorbed by a column density of N
-H similar to 3-5 x 10(22) cm(-2) or (2) reprocessed, with the nuclear sour
ce blocked and the X-rays Compton reflected in our direction by high column
density (greater than or equal to 10(24) cm(-2)) gas. The moderate equival
ent width of the Fe K alpha line favors the dual absorption model as the mo
st likely scenario. The 0.1-2.0 keV spectrum does not resemble the few time
s 10(6)-10(7) K thermal emission typically found in other elliptical galaxi
es, but instead is best described as nuclear X-rays leaking through a patch
y absorber or scattered in our direction by low-density, ionized gas plus a
15%-20% contribution from a thermal component, which is most likely due to
the galaxy. The absorption-corrected 2-10 keV luminosity of the nuclear so
urce is L-X similar to 8 x 10(41) ergs s(-1) or L-X similar to 2 x 10(43) e
rgs s(-1) for the dual-absorption and Compton-reflection models, respective
ly. The absorbing and H2O masing gases appear to be spatially separate in t
his galaxy.