We compare the results of the surveys of starless cores performed with CS (2-1) and (3-2) lines to study inward motions in the cores. The velocity shifts of the CS(3-2) and (2-1) lines with respect to $N_2H^+$ are found to correlate well with each other and to have similar number distributions, implying that, in many cores, systematic inward motions of gaseous material may occur over a range of density of at least a factor ${~}$4. Fits of the CS spectra to a 2-layer radiative transfer model in ten infall candidates suggest that the median effective line-of-sight speed of the inward-moving gas is ${~}0.07 km;s^{-l}$ for CS (3-2) and ${~} 0.04 km;s^{-l}$ for CS(2-1). Considering that the optical depth obtained from the fits is usually smaller in CS(3-2) than in (2-1) line, this may indicate that CS(3-2) usually traces inner, denser gas with greater inward motions than CS(2-1) implying that many of the infall candidates have faster infall toward the center. However, this conclusion may not be representative of all starless core infall candidates, due to the statistically small number analyzed here. Further line observations will be useful to test this conclusion.