In this paper, we indicate a possibility of utilizing the elastic scattering of the Dirac low energy (∼ 1 MeV) electron neutrinos (ν e 's) on the polarized electron target (PET) in testing the time reversal symmetry violation (TRSV). We consider a scenario in which the incoming ν e beam is the superposition of left chiral (LC) and right chiral (RC) states. LC ν e 's interact mainly by the standard V − A and small admixture of non-standard scalar S L , pseudoscalar P L , tensor T L interactions, while RC ones are only detected by the exotic V + A and S R , P R , T R interactions. In addition, one assumes that the spin polarization vector of the initial ν e 's is turned aside from its momentum, and due to this the nonvanishing transversal component of the ν e spin polarization appears. We compute the differential cross section as a function of the recoil electron azimuthal angle and scattered electron energy, and show how the interference terms between standard V − A and exotic S R , P R , T R couplings depend on the various angular correlations among the transversal ν e spin polarization, the polarization of the electron target, the incoming neutrino momentum and the outgoing electron momentum in the limit of relativistic ν e . We illustrate how the maximal value of recoil electrons azimuthal asymmetry and the asymmetry axis location of outgoing electrons depend on the azimuthal angle of the transversal component of the ν e spin polarization, both for the time reversal symmetry conservation (TRSC) and TRSV. Next, we display that the electron energy spectrum and polar angle distribution of the recoil electrons are also sensitive to the interference terms between V − A and S R , P R , T R couplings, proportional to the T-even and T-odd angular correlations among the transversal ν e polarization, the electron polarization of the target, and the incoming ν e momentum, respectively. Our modelindependent analysis is carried out for the flavor ν e 's. To a make such tests feasible, the intense (polarized) artificial ν e source, PET and the appropriate detector measuring the directionality of the outgoing electrons, and/or the recoil electrons energy with a high resolution have to be identified.