We report $^{75}$As nuclear magnetic resonance (NMR) studies on a new iron-based superconductor CaKFe$_4$As$_4$ with $T_{rm c}$ = 35 K. $^{75}$As NMR spectra show two distinct lines corresponding to the As(1) and As(2) sites close to the K and Ca layers, respectively, revealing that K and Ca layers are well ordered without site