Using the 18.8 pb-1 of data accumulated at LEP in 1990 and 1991 with the ALEPH detector, a direct test of neutral current CP-invariance is performed by a search for CP-odd correlations in Z decays to tau pairs where both tau decay modes are identified. No evidence for CP-violation is observed. The weak dipole moment of the tau has been measured to be d(tau)(m(Z)) = (1.3 +/- 1.4 +/- 0.1) x 10(-17)e.cm which results in an upper timit on the weak dipole moment of \d(tau)(m(Z))\ less-than-or-equal-to 3.7 x 10(-17)e.cm with 95% confidence level.
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