The dimensions of time constant in an L-R circuit is $[L/R] = [T]$ and in a C-R circuit is $[CR] = [T]$. Therefore, $[L]=[TR]$ and $[C]=[T/R]$. The dimensions of $C^2RL$ are $[(T/R)^2][R][TR] = [T^2/R^2][R^2T] = [T^3]$. So, the final dimension is $[M^0L^0T^3A^0]$.