conversation - Should I say "I don't know" or "That I don't know"?

When someone asks a question, is the reply, "That I don't know" correct? Or is the simpler "I don't know" a more correct or proper response?

Answer

Normally you just say:

I don’t know.

Sometimes when you want to draw attention to the thing unknown, you might venture to add an object:

I don’t know that.

But it would be rare indeed to apply inversion to put the now-important bit first:

That, I don’t know.