We present measurements of rotations of the optical polarization of blazars during the second year of operation of RoboPol, a monitoring programme of an unbiased sample of gamma-ray bright blazars specially designed for effective detection of such events, and we analyse the large set of rotation events discovered in two years of observation. We investigate patterns of variability in the polarization parameters and total flux density during the rotation events and compare them to the behaviour in a non-rotating state. We have searched for possible correlations between average parameters of the polarization-plane rotations and average parameters of polarization, with the following results: (1) there is no statistical association of the rotations with contemporaneous optical flares; (2) the average fractional polarization during the rotations tends to be lower than that in a non-rotating state; (3) the average fractional polarization during rotations is correlated with the rotation rate of the polarization plane in the jet rest frame; (4) it is likely that distributions of amplitudes and durations of the rotations have physical upper bounds, so arbitrarily long rotations are not realised in nature.