  We present the general formalism for studying CP-violating phenomena in the
production, mixing and decay of a coupled system of CP-violating neutral Higgs
bosons at high-energy colliders. Considering the Minimal Supersymmetric
Standard Model (MSSM) Higgs sector in which CP violation is radiatively induced
by phases in the soft supersymmetry-breaking third-generation trilinear squark
couplings and gaugino masses, we apply our formalism to neutral Higgs
production via {\bar b}b, gg and W^+ W^- collisions at the LHC. We discuss CP
asymmetries in the longitudinal and transverse polarizations of \tau^+ \tau^-
pairs. The signatures of CP violation are more prominent in the production via
gg and W^+ W^- than via {\bar b}b, and are resonantly enhanced when two (or all
three) neutral Higgs bosons are nearly degenerate with mass differences
comparable to their decay widths. Such scenarios occur naturally in the MSSM
for values of \tan\beta >~ 5 (30) and large (small) charged Higgs-boson masses.
We analyze representative examples with large mixing between the three neutral
Higgs bosons weighing about 120 GeV, that may exhibit observable CP asymmetries
even as large as 80%.
