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 δ of the flavor mixing and the matter parameter a. The two disentangled components, genuine A T;CP αβ and fake A T;CPT αβ , could be experimentally separated by the measurement of the two T asymmetries in matter (ν α ↔ ν β ) and (ν α ↔ν β ). For the (ν µ ↔ ν e ) transitions, the energy dependence of the new A T;CPT µe component is like the matter-induced term A CP;CPT µe 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 CP;T αβ and fake A CP;CPT αβ and A T;CPT αβ .