We investigate the polarimetric structure of three-dimensional (3D) light fields generated by an optical system from a random two-dimensional (paraxial) wave. In particular, we show that some central 3D polarimetric properties, e.g., the overall structure of the characteristic decomposition of the polarization matrix and whether the field is in a regular or nonregular polarization state, are determined by the geometry alone. The results are applied to tightly focused fields.