Summary: We propose to test \(P\)- and \(CP\)-symmetries with the process \(e^+ e^- \to J/\psi\to\Lambda\bar{\Lambda}\). The general form of the angular distribution of the process is derived and several observables for the proposed test are introduced. With these observables one can distinguish the effects of \(P\)-violations in the production of \(J/\psi\) from its decay into a pair of \(\Lambda\bar{\Lambda}\). Numerical estimations for proposed asymmetries of \(P\)-violation due to \(Z\) exchange in SM are given. Our results show that BESIII has reached the sensitivity to probe these effects. At the proposed super-tau-charm factory with much enhanced luminosity it will be able to test the SM predictions with high precision. \(CP\) violating effect in \(J/\psi\to\Lambda\bar{\Lambda}\) can also be tested. In particular, BESIII data already reached the sensitivity to prove \(CP\) violating effect due to current upper limit of electric dipole moment of \(\Lambda\). At the proposed super-tau-charm factory the upper limit can be improved by an order of magnitude.