The anomalous weak dipole moments of the τ lepton are measured in a data sample collected by ALEPH from 1990 to 1995 corresponding to an integrated luminosity of 155 pb-1. Tau leptons produced in the reaction e+e−→τ+τ− at energies close to the Z mass are studied using their semileptonic decays to π , ρ , a1→π2π0 or a1→3π . The real and imaginary components of both the anomalous weak magnetic dipole moment and the CP-violating anomalous weak electric dipole moment, Reμτ , Imμτ , Redτ and Imdτ , are measured simultaneously by means of a likelihood fit built from the full differential cross section. No evidence of new physics is found. The following bounds are obtained (95% CL): |Reμτ|<1.14×10−3 , |Imμτ|<2.65×10−3 , |Redτ|<0.91×10−3 , and |Imdτ|<2.01×10−3 .