We investigate gap states in a series of nonmagnetic ZnO films grown by molecular beam epitaxy (MBE) and pulsed laser deposition (PLD) using magnetic circular dichroism. This technique is shown to be sensitive enough to investigate defect states in thin films of disordered wide-gap semiconductors by differentiating between a loss of transmission due to scattering and absorption. The method is first applied to Zn- and O-terminated films grown by MBE. The O-terminated film shows a broad peak centred at ~2.4 eV which corresponds to the green PL signal, whereas the Zn-terminated film shows a magnetic circular dichroism (MCD) signal that increases slowly with energy. The method was then extended to PLD films. Oxygen vacancy states in both MBE and PLD-grown films were identified, and the introduction of low concentrations of Al was shown to quench the MCD signal at low energy by neutralising the paramagnetic oxygen vacancies. In PLD-grown ZnAlO we observed a negative MCD that increased in magnitude as the energy approached the band edge indicating a much more pronounced spin-split impurity and conduction band. These examples illustrate the versatility of the MCD technique in identifying gap states in a variety of different types of ZnO samples.