The polarization of radiation emitted in spectral lines provides an important diagnostic tool when the relationship between the mechanisms that excite the atomic or molecular energy levels and the polarization is understood. The gas is assumed to be in statistical equilibrium and we present a general formulation of the theory in which all collisional and radiative excitation and decay processes are included. The colliding particles are assumed to have an anisotropic velocity distribution with cylindrical symmetry and the theory allows for rotation of the axis of observation. Some assumptions made in previous work are removed by the introduction of a completely quantum-mechanical description of the collision processes. Such a theory is important both for the detailed analysis of collision experiments in the laboratory and for the analysis of spectra emitted by astrophysical plasmas.