We analyzed multiline observations of a quiescent prominence from the slit spectrograph located at the Ondřejov Observatory. Dopplergrams and integrated intensity maps of the whole prominence were obtained from observations in six spectral lines: Ca II H, Hϵ, Hβ, He I D3, Hα, and Ca II IR. By combining integrated intensity maps with non-LTE radiative-transfer modeling, we carefully identified areas in an optically thin regime. The comparison of the Doppler-velocity maps and scatterplots from different lines shows the existence of differences in the velocity of ions and neutrals called velocity drift. The drift is of a local nature, present mostly at prominence edges in the area with a large velocity gradient, as can be tentatively expected based on multifluid MHD models. We could not explore the time evolution of the drift, since our data set consists of a single scan only. Our paper brings another contribution to a rather controversial problem of the detection of multifluid effects in solar prominences.