We investigate the possibility of determining local dispersion characteristics of Love waves using seismograms of transverse acceleration and rotation rate around a vertical axis recorded at the same site. Assuming plane-wave propagation, phase velocity information is contained in the frequency-dependent amplitude ratio of the two different types of ground motion. We perform tests of this method using real measurements from a ring laser system and a broadband seismometer at the geodetic observatory Wettzell in southeast Germany as well as synthetic seismograms computed by normal mode summation. While general dispersion characteristics can be recovered, we show that the contribution of overtones impedes the use of this method for structural inversion. To extract the structural information contained in collocated measurements of rotations and translations, a full waveform inversion is necessary.