  Hidden magnetic order of Sr$_2$Ir$_{1-x}$Rh$_x$O$_4$, $x = 0.05$ and 0.1, has
been studied using muon spin relaxation spectroscopy. In zero applied field and
weak longitudinal fields ($\mu_0H_L \lesssim 2$~mT), muon spin relaxation data
can be well described by exponentially-damped static Lorentzian Kubo-Toyabe
functions, indicating that static and dynamic local fields coexist at each muon
site. For $\mu_0H_L \gtrsim 2$~mT, the static rate is completely decoupled, and
the exponential decay is due to dynamic spin fluctuations. In both zero field
and $\mu_0H_L = 1$--2~mT, the temperature dependencies of the exponential muon
spin relaxation rate exhibit maxima at 215~K for $x = 0.05$ and 175~K for $x =
0.1$, suggesting critical slowing down of electronic spin fluctuations. The
field dependencies of the dynamic spin fluctuation rates can be well described
by the Redfield relation. The correlation time of this electronic spin
fluctuation is in the range of~2--5~ns for Sr$_2$Ir$_{0.9}$Rh$_{0.1}$O$_4$, and
shorter than 2~ns for Sr$_2$Ir$_{0.95}$Rh$_{0.05}$O$_4$. The rms fluctuating
field is on the order of 1 mT, which is consistent with the polarized neutron
diffraction cross-section.
