Measurements of the tau lepton polarization and forward-backward polarization asymmetry near the Z(0) resonance using the OPAL detector are described. The measurements are based on analyses of tau -->e nu (e)nu (tau), tau --> mu nu (mu)nu (tau), tau --> pi nu (tau), tau --> rho nu (tau) and tau -->a(1)nu (tau) decays from a sample of 144,810 e(+) e(-) --> tau (+) tau (-) candidates corresponding to an integrated luminosity of 151 pb(-1). Assuming that the tau lepton decays according to V-A theory, we measure the average tau polarization near roots = M-z to be = (-14.10 +/- 0.73 +/-0.55)% and the tau polarization forward-backward asymmetry to be A(pol)(FB) = (-10.55 +/-0.76 +/-0.25)%, where the first error is statistical and the second systematic. Taking into account the small effects of the photon propagator, photon-Z(0) interference and photonic radiative corrections, these results can be expressed in terms of the lepton neutral current asymmetry parameters: A(tau) = 0.1456 +/- 0.0076 +/- 0.0057 A(e) = 0.1454 +/- 0.0108 +/- 0.0036 These measurements are consistent with the hypothesis of lepton universality and combine to give A(t) = 0.1455 +/-0.0073. Within the context of the Standard Model this combined result corresponds to = 0.23172 +/-0.00092. Combing these results with those from the other OPAL neutral current measurements yields a value of = 0.23211 +/-0.00068.