We conducted series of experiments on observing a Stark-type effect in superfluid $^4$He in presence of relative laminar flows of the normal and superfluid components. It is designed a measurement cell which allows us to simultaneously create hydrodynamic flows in the liquid and to carry out high-frequency radio-measurements at external electric field. We used a dielectric disk resonator that made possible to cover a wide frequency range. In our experiments it was registered the spectrum of the dielectric disk resonator modes, as well as narrow lines of absorption of a microwave radiation in He II on its background and in different conditions. We discovered that having in the liquid helium a relative motion of the normal and superfluid fractions in the temperature range of 1.4$div$2.17 K the narrow line of absorption/radiation is observed in the EM spectrum, the frequency of which - 180 GHz - corresponds to the roton minimum. This line splits in a constant electric field. Note that in a weak electric field the value of splitting depends linearly on the electric field strength, i.e. the linear Stark effect is detected. It is found that with the external electric field increasing both split lines are displaced towards more low frequencies side. The obtained data set could be described by an empirical formula, taking into account as the linear part of the Stark effect, as well as a quadratic addition, related to the polarization part. The data point out on having particles or excitations in the liquid helium with the dipole moment $sim 10^{-4}$ D, that in four order less of the characteristic dipole moment of polar molecules. The comparison of our findings to values of the electric dipole moment (EDM) of elementary particles and nuclei is also performed. We sum up with brief discussion of extensions of the known theoretical models and possible mechanisms of the EDM production.
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