  We present new optical broad-band (UBVRI) aperture polarimetric observations
of 53 post-asymptotic giant branch (AGB) stars selected to exhibit a large
near-infrared excess. 24 out of the 53 stars (45% of our sample) are presented
for the first time. A statistical analysis shows four distinctive groups of
polarized post-AGB stars: unpolarized or very lowly polarized (degree of
polarization or DoP < 1%), lowly polarized (1% < DoP < 4%), moderately
polarized (4% < DoP < 8%) and highly polarized (DoP > 8%). 23 out of the 53
(66%) belong to the first group, 10 (19%) to the second, five (9%) to the third
and only three (6%) to the last group.
  Approximately, 34% of our sample was found to be unpolarized objects, which
is close to the percentage of round planetary nebulae. On average, the low and
moderate groups show a wavelength-dependent polarization that increases towards
shorter wavelength, implying an intrinsic origin of the polarization, which
signifies a Rayleigh-like scattering spectrum typical for non-symmetrical
envelopes composed principally of small dust grains. The moderately polarized
stars exhibit higher K-W3 and W1-W3 colour indices compared with the group of
lowly polarized stars suggesting a possible relation between DoP and mass-loss
rate. Moreover, they are found to be systematically colder (redder in B-V),
which may be associated with the condensation process close to these stars that
results in higher degree of polarization. We also provide evidence that
multiple scattering in optically thin polar outflows is the mechanism that
gives high DoP in post-AGB stars with a bipolar or multi-polar envelopes.
