Scattering of charge carriers by impurity ions in quasi-two-dimensional electronic systems is investigated. The dependences of the longitudinal and transverse components of the relaxation time on the wave vector components and the screening length are analyzed. The anisotropy of electrical conductivity of a degenerate quasi-two-dimensional electron gas is studied as a function of the ratio between the energy at the Fermi level and the miniband width, the impurity concentration, and the lattice constant.