The hydride reduction of a tetragonal layered perovskite LaSrCoO4 is known to yield orthorhombic LaSrCoO3H0.7 with a complete hydride/oxide order within the ab plane. In this study, epitaxial thin films of LaSrCoO4 with a-axis and c-axis orientations have been deposited on (100) and (001) LaSrAlO4 (LSAO) substrates, respectively, and allowed to react with hydride to convert into oxyhydrides. X-ray diffraction, secondary ion mass spectroscopy and thermal desorption spectroscopy experiments indicate that both films are topochemically reduced and can integrate hydride ions with a chemical composition close to that obtained for the powder. A significant reduction in the a-axis was observed for the a-axis oriented LaSrCoO3H0.7 film, indicating hydride/oxide order, as previously reported. In contrast, the c-axis oriented LaSrCoO3H0.7 film remains tetragonal, suggesting hydride/oxide disorder. These results demonstrate that strain engineering can lead to new materials with designed anion arrangement in mixed anion materials.