We report $^{75}$As nuclear magnetic resonance (NMR) measurements of single-crystalline Ca(Fe$_{1-x}$Co$_x$)$_2$As$_2$ ($x$ = 0.023, 0.028, 0.033, and 0.059) annealed at 350~$^{circ}$C for 7 days. From the observation of a characteristic shape of $^{75}$As NMR spectra in the stripe-type antiferromagnetic (AFM) state, as in the case of $x$ = 0 ($T_{rm N}$ = 170 K), clear evidence for the commensurate AFM phase transition with the concomitant structural phase transition is observed in $x$ = 0.023 ($T_{rm N}$ = 106 K) and $x$ = 0.028 ($T_{rm N}$ = 53 K). Through the temperature dependence of the Knight shifts and the nuclear spin lattice relaxation rates (1/$T_1$), although stripe-type AFM spin fluctuations are realized in the paramagnetic state as in the case of other iron pnictide superconductors, we found a gradual decrease of the AFM spin fluctuations below a crossover temperature $T^*$ which was nearly independent of Co-substitution concentration, and is attributed to a pseudogap-like behavior in the spin excitation spectra of these systems. The $T^*$ feature finds correlation with features in the temperature-dependent inter-plane resistivity, $rho_c(T)$, but not with the in-plane resistivity $rho _a (T)$. The temperature evolution of anisotropic stripe-type AFM spin fluctuations are tracked in the paramagnetic and pseudogap phases by the 1/$T_1$ data measured under magnetic fields parallel and perpendicular to the $c$ axis. Based on our NMR data, we have added a pseudogap-like phase to the magnetic and electronic phase diagram of Ca(Fe$_{1-x}$Co$_x$)$_2$As$_2$.
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