  We report observations of 47 candidate protostars in two optically thick
lines (H2CO 212-111 and CS 2-1) and one optically thin line (N2H+ 1-0) using
the IRAM 30-m, SEST 15-m, and Haystack 37-m radio telescopes. The sources were
selected from the redness of their spectra (Tbol < 200 K) and their near
distance (d < 400 pc). Most of the sources have asymmetric optically thick
lines. The observed distribution of velocity differences, deltaV =
(Vthick-Vthin)/FWHMthin, is skewed toward negative (blue-shifted) velocities
for both the H2CO and CS samples. This excess is much more significant for
Class 0 than for Class I sources, suggesting that we detect infall motions
toward Class 0 and not toward Class I sources. This indicates a difference in
the physical conditions in the circumstellar envelopes around Class I and Class
0 sources, but does not rule out the presence of infall onto Class I sources by
e.g. lower opacity gas. Bipolar outflows alone, or rotation alone, cannot
reproduce these statistics if the sample of sources has randomly oriented
symmetry axes. We identify 15 spectroscopic infall candidates, of which 6 are
new. Most of these infall candidates have primarily turbulent rather than
thermal motions, and are associated with clusters rather than being isolated.
