We present the results of our BVR-band photometric and R-band polarimetric observations of ∼40 stars in the periphery of the dark cloud CB54. From different photometric data, we estimate E(B - V) and E(J - H). After involving the data from other sources, we discuss the extinction variations towards CB54. We reveal two main dust layers: a foreground (E(B - V) ≍ 0.1 mag) at ∼200pc and an extended layer ( $E(B-V) \gtrsim 0.3$ mag) at ∼1.5kpc, with CB54 belonging to the latter. Based on these results, we consider the reason for rather random polarization map observed by us for CB54. We find that the foreground is characterized by low polarization ( $P \lesssim 0.5$ percent) and the magnetic field parallel to the Galactic plane. The extended layer shows high polarization (P up to 5-7percent). We suggest that the field in this layer is nearly perpendicular to the Galactic plane and both layers are essentially inhomogeneous. This allows us to generally explain the randomness of polarization vectors around CB54. The data primarily observed by us for CB54, then by Sen etal. (2000, 2010) for three dark clouds CB3, CB25, CB39 and by other authors for a region including B1 cloud are analysed to explore any correlation between polarization, the near-IR (E(J - H)) and optical (E(B - V)) excesses, and the distance to the background stars. If polarization and extinction are caused by the same set of dust particles, we should expect good correlations. However, we find that for all the clouds the correlations are not strong.