The DANSS experiment aims to search for sterile neutrinos. It is a compact neutrino spectrometer located at the Kalinin Nuclear Power Plant close to the core of the industrial power reactor. The detector records about 3000-4000 events per day after subtracting the background depending on the position. The significant contribution to background events is made by neutrons from the interaction of cosmic muons formed in the materials surrounding the detector volume. In this work preliminary results of neutron signal spectra are presented.