  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.
