This paper presents velocity and angular distribution measurements of the products of N2O4 photodissociated at 193 nm. The data show evidence for only N-N bond fission, with no significant branching to N-O bond fission or NO elimination products. The translational energy distribution of the N-N bond fission products is bimodal, indicating that at least two different NO2 + NO2 product channels contribute significantly to the observed products. Both product channels have an anisotropy parameter of beta = 1.7 +/- 0.2. Using a Franck-Condon-like sudden analysis, we tentatively assign the two fragmentation channels observed as NO2((X) over tilde(2)A(1)) + NO2(1(4)B(2)/1(4)A(2)) and NO2((X) over tilde(2)A(1)) + NO2(2(2)B(2)). TO further characterize the system we present ab initio calculations (at the level of configuration interaction with single excitations) of the relevant excited states of N2O4. The data considered together with the calculations suggest a model for the product branching in which there is spin-orbit coupling in the Franck-Condon region between the excited state, which has mixed singlet pi pi* and n sigma* character, and a state with (3)pi sigma* character. Branching to the NO2((X) over tilde) + NO2(1(4)B(2)/1(4)A(2)) channel occurs upon intersystem crossing to the triplet surface, and formation of the pi pi* diabatic products NO2((X) over tilde) + NO2(2(2)B(2)) occurs from the singlet pi pi* state nonadiabatic dynamics. Finally, we note that the observed parallel photofragment anisotropy, unexpected for pi pi* electronic excitation of N2O4, likely results from vibronic coupling with a sigma sigma* electronic state.