  Observables of neutrino oscillations in matter have, in general,
contributions from the effective matter potential. It contaminates the CP
violation asymmetry adding a fake effect that has been recently disentangled
from the genuine one by their different behavior under T and CPT. Is the
genuine T-odd CPT-invariant component of the CP asymmetry coincident with the T
asymmetry? Contrary to CP, matter effects in uniform matter cannot induce by
themselves a non-vanishing T asymmetry; however, the question of the title
remained open. We demonstrate that, in the presence of genuine CP violation,
there is a new non-vanishing CP-even, and so CPT-odd, component in the T
asymmetry in matter, which is of odd-parity in both the phase $\delta$ of the
flavor mixing and the matter parameter $a$. The two disentangled components,
genuine $A^\mathrm{T;CP}_{\alpha\beta}$ and fake
$A^\mathrm{T;CPT}_{\alpha\beta}$, could be experimentally separated by the
measurement of the two T asymmetries in matter ($\nu_\alpha \leftrightarrow
\nu_\beta$) and ($\bar\nu_\alpha \leftrightarrow \bar\nu_\beta$). For the
($\nu_\mu \leftrightarrow \nu_e$) transitions, the energy dependence of the new
$A^\mathrm{T;CPT}_{\mu e}$ component is like the matter-induced term
$A^\mathrm{CP;CPT}_{\mu e}$ of the CP asymmetry which is odd under a change of
the neutrino mass hierarchy. We have thus completed the physics involved in all
observable asymmetries in matter by means of their disentanglement into the
three independent components, genuine $A^\mathrm{CP;T}_{\alpha\beta}$ and fake
$A^\mathrm{CP;CPT}_{\alpha\beta}$ and $A^\mathrm{T;CPT}_{\alpha\beta}$.
