In astrophysical systems with partially ionized plasma the motion of ions is governed by the magnetic field while the neutral particles can only feel the magnetic fields Lorentz force indirectly through collisions with ions. The drift in the velocity between ionized and neutral species plays a key role in modifying important physical processes like magnetic reconnection, damping of magnetohydrodynamic waves, transport of angular momentum in plasma through the magnetic field, and heating. This paper investigates the differences between Doppler velocities of calcium ions and neutral hydrogen in a solar prominence to look for velocity differences between the neutral and ionized species. We simultaneously observed spectra of a prominence over an active region in H I 397 nm, H I 434 nm, Ca II 397 nm, and Ca II 854 nm using a high dispersion spectrograph of the Domeless Solar Telescope at Hida observatory, and compared the Doppler velocities, derived from the shift of the peak of the spectral lines presumably emitted from optically-thin plasma. There are instances when the difference in velocities between neutral atoms and ions is significant, e.g. 1433 events (~ 3 % of sets of compared profiles) with a difference in velocity between neutral hydrogen atoms and calcium ions greater than 3sigma of the measurement error. However, we also found significant differences between the Doppler velocities of two spectral lines emitted from the same species, and the probability density functions of velocity difference between the same species is not significantly different from those between neutral atoms and ions. We interpreted the difference of Doppler velocities as a result of motions of different components in the prominence along the line of sight, rather than the decoupling of neutral atoms from plasma.