Fe-57 Mossbauer spectra at different temperatures between similar to 5 and similar to 300 K were measured on an oriented mosaic of single crystals of CaKFe4As4. The data indicate that CaKFe4As4 is a well formed compound with narrow spectral lines, no traces of other, Fe -containing, secondary phases in the spectra and no static magnetic order. There is no discernible feature at the superconducting transition temperature in any of the hyperfine parameters. The temperature dependence of the quadrupole splitting approximately follows the empirical 'T3/2 law'. The hyperfine parameters of CaKFe4As4 are compared with those for KFe2As2 measured in this work, and the literature data for CaFe2As2, and were found to be in between those for these two, ordered, 122 compounds, in agreement with the gross view of CaKFe4As4 as a structural analog of KFe2As2 and CaFe2As2 that has alternating Ca-and K-layers in the structure.