Optical conductivity spectra $sigma_1(omega)$ of paramagnetic CaRuO$_3$ are investigated at various temperatures. At T=10 K, it shows a non-Fermi liquid behavior of $sigma_1(omega)sim 1/{omega}^{frac 12}$, similar to the case of a ferromagnet SrRuO$_3$. As the temperature ($T$) is increased, on the other hand, $sigma_1(omega)$ in the low frequency region is progressively suppressed, deviating from the $1/{omega}^{frac 12%}$-dependence. Interestingly, the suppression of $sigma_1(omega)$ is found to scale with $omega /T$ at all temperatures. The origin of the $% omega /T$ scaling behavior coupled with the non-Fermi liquid behavior is discussed.