Epitaxial thin films of CuMnAs have recently attracted attention due to their potential to host relativistic antiferromagnetic spintronics and exotic topological physics. Here we report on the structural and electronic properties of a tetragonal CuMnAs thin film studied using scanning tunneling microscopy (STM) and density functional theory (DFT). STM reveals a surface terminated by As atoms, with the expected semi-metallic behavior. An unexpected zigzag step edge surface reconstruction is observed with emerging electronic states below the Fermi energy. DFT calculations indicate that the step edge reconstruction can be attributed to an As deficiency that results in changes in the density of states of the remaining As atoms at the step edge. This understanding of the surface structure and step edges on the CuMnAs thin film will enable in-depth studies of its topological properties and magnetism.