  We carried out $^{75}$As nuclear magnetic resonance (NMR) measurements on the
trigonal CaMn$_2$As$_2$ and SrMn$_2$As$_2$ insulators exhibiting
antiferromagnetic (AFM) ordered states below N\'eel temperatures $T_{\rm N}$ =
62 K and 120 K, respectively. In the paramagnetic state above $T_{\rm N}$,
typical quadrupolar-split $^{75}$As-NMR spectra were observed for both systems.
The $^{75}$As quadrupolar frequency $\nu_{\rm Q}$ for CaMn$_2$As$_2$ decreases
with decreasing temperature, while $\nu_{\rm Q}$ for SrMn$_2$As$_2$ increases,
showing an opposite temperature dependence.In the AFM state, the relatively
sharp and distinct $^{75}$As NMR lines were observed in SrMn$_2$As$_2$ and the
NMR spectra were shifted to lower fields for both magnetic fields $H$ $||$ $c$
axis and $H$ $||$ $ab$ plane, suggesting that the internal fields $B_{\rm int}$
at the As site produced by the Mn ordered moments are nearly perpendicular to
the external magnetic field direction. No obvious distribution of $B_{\rm int}$
was observed in SrMn$_2$As$_2$, which clearly indicates a commensurate AFM
state. In sharp contrast to SrMn$_2$As$_2$, broad and complex NMR spectra were
observed in CaMn$_2$As$_2$ in the AFM state, which clearly shows a distribution
of $B_{\rm int}$ at the As site, indicating an incommensurate state. From the
analysis of the characteristic shape of the observed spectra, the AFM state of
CaMn$_2$As$_2$ was determined to be a two-dimensional incommensurate state
where Mn ordered moments are aligned in the $ab$ plane. A possible origin for
the different AFM states in the systems was discussed. Both CaMn$_2$As$_2$ and
SrMn$_2$As$_2$ show very large anisotropy in the nuclear spin-lattice
relaxation rate 1/$T_1$ in the paramagnetic state. 1/$T_1$ for $H$ $||$ $ab$ is
much larger than that for $H$ $|| $c$, indicating strong anisotropic AFM spin
fluctuations in both compounds.
