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We prove that, in any flavor transition, neutrino oscillation CP violatingasymmetries in matter have two disentangled components: (a) a CPT-oddT-invariant term, non-vanishing iff there are interactions with matter; (b) aT-odd CPT-invariant term, non-vanishing iff there is genuine CP violation. Asfunction of the baseline, these two terms are distinct L-even and L-oddobservables, respectively. In the experimental region of terrestrialaccelerator neutrinos, we calculate their approximate expressions from which weprove that, at medium baselines, the CPT-odd component is small and nearly$\delta$-independent, so it can be subtracted from the experimental CPasymmetry as a theoretical background, provided the hierarchy is known. At longbaselines, on the other hand, we find that (i) a Hierarchy-odd term in theCPT-odd component dominates the CP asymmetry for energies above the firstoscillation node, and (ii) the CPT-odd term vanishes, independent of the CPphase $\delta$, at E = 0.92 GeV(L/1300 km) near the second oscillation maximum,where the T-odd term is almost maximal and proportional to $\sin\delta$. Ameasurement of the CP asymmetry in these energy regions would thus provideseparate information on (i) the neutrino mass ordering, and (ii) directevidence of genuine CP violation in the lepton sector.

Disentangling genuine from matter-induced CP violation in neutrino oscillations