We consider influence of nonlocal (retardation) effects caused by the finite value of the speed of light on collective emission of a single photon by atomic ensembles. Using a fully quantum mechanical description of light and atoms we obtain an evolution equation for the atomic system that takes into account retardation. We found an exact analytical solution of this equation for the atomic slab geometry that yields insight on how the crossover between local and nonlocal dynamics occurs. In particular, it shows that initially nonlocal evolution, accompanied by collective oscillations of atomic population, becomes local at large time. In addition, atomic excitation in some parts of the sample rises above its initial value. We propose an experiment in which the transition between local and nonlocal regimes can be observed by increasing the size of the atomic sample or atomic density.