Let $X$ be an algebraic variety over $\mathbb{C}$. If $X$ is smooth, the étale cohomology $H^p\_{\textrm{ét}}(X,\mathbb{Z}/n)$ is isomorphic to the singular cohomology $H^p(X(\mathbb{C}),\mathbb{Z}/n)$. What is the situation if $X$ is not smooth? Are there counter-examples? 



Étale cohomology versus classical cohomology
In Katz's review of $\ell$-adic cohomology in the first "Motives" volume, this isomorphism is stated without any smoothness assumptions, with a reference to SGA4, XVI 4.1 (which I don't have easily available). 


