The existence of the dielectric constant epsilon is investigated for fluids composed of nonlinear rigid polar molecules. The investigation is performed using the functional-derivative approach previously employed to establish sufficient conditions for the existence of epsilon in fluids of linear (axially symmetric) molecules. It is shown that these same conditions are sufficient for nonlinear molecules of arbitrary symmetry. An expression for epsilon in terms of the direct correlation function emerges automatically from the development. This expression, which involves the inversion of a 3 x 3 matrix, is a slight generalization of one obtained earlier by Hoye and Stell using an entirely different approach.