The infinite hierarchy of differential-recurrence relations for ensemble averages of the spherical harmonics pertaining to the noninertial rotational Brownian motion of an ensemble of polar and anisotropically polarizable molecules in a strong external de electric field is derived by averaging the underlying Langevin equation. This procedure avoids recourse to the Fokker-Planck equation, the solution of which involves complicated mathematical manipulations. By calculating the Laplace transforms of the relaxation functions for the dynamic Kerr effect of, symmetric top molecules, two equilibrium correlation functions are established, thus allowing one to express the corresponding birefringence ac responses by using linear response theory. Exact analytic solutions for the spectra of these correlation functions and relaxation times are first calculated for two limiting cases, namely, pure induced dipole moments and pure permanent moments, using the continued fraction method. The general case where both types of moments are taken into account, is then considered using matrix continued fractions. Furthermore, exact analytical expressions for the Kerr effect relaxation time are also derived in terms of integrals (which are evaluated exactly) and compared with the matrix continued fraction result. Plots of the relaxation time are presented for various values of the parameters xi and sigma characterizing the permanent and the induced dipole moments. Features of the relaxation behavior are emphasized in figures showing the real and imaginary parts of the spectra of the birefringence function. Moreover, Cole-Cole diagrams are presented for various values of xi and sigma in order to see how they deviate from the Debye-like spectra.