I have originally posted this question on math.SE, but it received little attention, so I repost it here.

Let $U\subset \mathbb{C}^{n}$ and $V\subset \mathbb{C}^{m}$ be open and connected. Let $\Phi:U\to V$ be a holomorphic map.

Is it true that there is a non-zero holomorphic function $w$ on a neighbourhood of $\Phi(U)$, which vanishes at every critical value of $\Phi$?

If this is wrong, is there any other refinement of Sard's theorem for the holomorphic maps between complex domains?