Using the ARGUS detector at the e+e- storage ring DORIS II, we have searched for the real and imaginary part of the electric dipole formfactor d_tau of the tau lepton in the production of tau pairs at q^2=100 GeV^2. This is the first direct measurement of this CP violating formfactor. We applied the method of optimised observables which takes into account all available information on the observed tau decay products. No evidence for CP violation was found, and we derive the following results: Re(d_tau)=(1.6+-.9)*10^(-16) ecm and Im(d_tau)=(-0.2+-0.8)*10^(-16) ecm, where statistical and systematic errors have been combined.
Electric dipole moment in E(electric charge)*CM units. Systematic and statistical errors are added in quadrature.
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