Let $S$ be a projective surface over an algebraically closed field. Suppose that $q(S)=h^1(\mathcal O_S)=0$ and $P_2(S)=h^0(\mathcal O_S(2K_S))=0$. If $S$ is smooth, Castelnuovo's rationality criterion (proved by Zariski in characteristic p) tells us that $S$ is rational.

Does this extend to singular surfaces if the characteristic is 0? I'm happy if it extends only to 'some' singular surfaces (e.g. canonical).

I have looked for this in the literature but I haven't found anything to prove it or disprove it. I assume someone has asked this question before (although not in MO, it seems).