If we have a singularity AI then we don't need CAPTCHAs: For all intents and purposes an AI is equal or superior to humans, there is no distinction to be made. The Turing Test is a form of CAPTCHA.

Also, one could make CAPTCHA's incredibly hard. Humans and dumb computers won't be able to solve it, and singular AI's get a pass. So give access to anyone who isn't able to solve the CAPTCHA and redirect the singularity AIs to google.com :).

Finally, the singular AI could create a CAPTCHA which separates humans from AI. The problem of separating humans from AI will quickly become too difficult for humans to solve.