I'd suggest a non-verbal cue, something subtle (like wiggling a finger) that the bird will recognize, but humans won't really notice, or which could be blocked from their view. That way you can ask any number of questions and cue a "no" response.
(Extra points if you can also train a nod for "yes.")
That way you can script whole funny little conversations.
"Did you shred the curtains?"
No.
"Oh really? Then who did? Was it [other pet]?
No.
Was it a mouse?
No.
Was it [guest observing interaction]?
Yes.
You're telling me that [guest] snuck in the house last week and shredded the curtains?
Yes.
And they just happened to make the damage look like a bird did it?
Yes.
(This isn't the best example, but you get the idea. A yes/no signal has unlimited comedic potential).