Suppose $X$ is a normal complex space with at most singularities, can we say any locally free sheaf on it is Cohen-Macauly? Recall that a coherent sheaf $\mathcal{F}$ over $X$ is called (maximal) Cohen-Macaulay if $depth_{\mathcal{O}_x}(\mathcal{F}_x) = \dim\mathcal{O}_x$ for any $x\in X$, where $\mathcal{O}_x$ is the local ring of $X$ at $x$.

How badly the singularities can the complex space $X$ possess to remain the above property?

Thanks!