The DANSS detector (Alekseev et al. in JINST 11:P11011, 2016) is located directly below a commercial reactor core at the Kalinin Nuclear Power Plant. Such a position provides an overburden about 50 m.w.e. in vertical direction. In terms of the cosmic rays it occupies an intermediate position between surface and underground detectors. The sensitive volume of the detector is a cubic meter of plastic scintillator with fine segmentation and combined PMT and SiPM readout, surrounded by multilayer passive and active shielding. The detector can reconstruct muon tracks passing through its sensitive volume. The main physics goal of the DANSS experiment implies the antineutrino spectra measurements at various distances from the source. This is achieved by means of a lifting platform so that the data is taken in three positions – 10.9, 11.9 and 12.9 meters from the reactor core. The muon data were collected for nearly four calendar years. The overburden parameters ⟨ E thr cos θ ⟩ and ⟨ E thr ⟩ , as well as the temperature and barometric correlation coefficients are evaluated separately for the three detector positions and, in each position, in three ranges of the zenith angle – for nearly vertical muons with cos θ > 0.9 , for nearly horizontal muons with cos θ < 0.36 , and for the whole upper hemisphere.