An examination of the intensity, energy spectrum, and spatial distribution of the diffuse γ radiation observed by SAS 2 away from the galactic plane in the energy range above 35 MeV has revealed no evidence supporting a cosmic ray halo surrounding the galaxy in the general shape of a sphere. The diffuse γ radiation does consist of two components. One component is related to the galactic disk on the basis of its correlation with the 21-cm measurements, the continuum radio emission, and galactic coordinates. Further its energy spectrum is similar to that in the plane, and its intensity distribution joins smoothly to the intense radiation from the plane. The other component appears isotropic, at least on a coarse scale, and has a steep energy spectrum. The degree of isotropy which has been established for the “isotropic” radiation and the steep energy spectrum, which distinguishes it from the galactic disk radiation, place strong constraints on galactic halo models for the origin of this component. Theoretical models involving a galactic halo have generally postulated a halo with dimensions of the order of the Galaxy and hence a radius, at least in the plane, of about 15 kpcs. Since the Sun is about 10 kpc from the galactic center, if such a halo exists and is responsible for the γ rays (through, for example, black body Compton radiation), a very marked anisotropy would be seen, with the γ ray intensity from the general direction of the galactic center being much larger than that from the same latitudes in the anticenter direction. In fact, no such anisotropy is seen; specifically the ratio of the average intensity in the (300° < ℓ < 60°, 20° < |b| < 40°) region to that in the (100° < ℓ < 250°, 20° < |b| < 40°) region was found to be 1.10±0.19 compared to a calculated value for a model with a uniform cosmic ray sphere with a 15 kpc radius of 2.85. The ratio between the average γ-ray intensity from regions with |b| < 60° to that from 20° < |b| < 40° is found to be 0.87±0.09. If the region is assumed to be spherical, but with a larger radius and a uniform cosmic ray density, the upper limit (2σ) set for the anisotropy demands that the radius be at least 45 kpc. An extragalactic origin for the isotropic component currently appears to be a more plausible explanation.