$\mathrm{CP}$-violating but $P$-preserving electromagnetic couplings of the $W^{\pm }$ and $Z^0$

We show that the electroweak gauge bosons $W^{\pm }$ and $Z^0$ can have $\mathrm{CP}$-violating (but $P$-preserving) couplings to the photon and $Z^0$ boson that are very weakly bounded by current limits on fermion electric dipole moments, and by present data from the CERN $e^{+}{e}^{-}$ collider LEP. They nevertheless can be large enough to be detectable, for instance, in gauge-boson pair production at LEP 200.