Let X be a DM stack over a scheme S. X is called tame if its automorphism groups are of order invertible on S. For example, every DM stack over a field of characteristic zero is tame.
If X is tame and smooth over S, then the (relative) inertia stack $I_{X/S}$ is smooth over S. This is because $I_{X/S}$ can be decomposed as the disjoint union of $Map^{repr}(B\mathbb{Z}/n, X)$, stack of representable maps $B\mathbb{Z}/n \to X$, over integers $n$ invertible on $S$. Each $G=\mathbb{Z}/n$ is linearly reductive over $S$ so these mapping stacks are smooth (the cotangent complex is the $G$-invariants of the cotangent complex $L_X$ pulled back to $BG$).