Documented: Gateless Barrier (Wumen guan), case 1, compiled 1228 by Wumen Huikai: a monk asks Zhaozhou Congshen whether a dog has Buddha-nature; Zhaozhou answers Mu. Wumen's commentary forbids both yes and no readings: it is not the nothing of non-existence, carry it like a hot iron ball. The koan became the standard first barrier of Rinzai training in China, Korea, and Japan.
The complication documented in the sources: the Zhaozhou dialogue record contains both versions, Mu to one monk and U, has-it, to another, which is either a contradiction, a later interpolation, or the point. Wumen chose the Mu. Chan scholarship has argued about the double answer for centuries, and the choosing is itself part of the case's history.
The linguistic note: mu, wu in Mandarin, is an ordinary negator, without, non-, have-not, and Daoist texts used wu as a cosmological term, the nameless non-being from which being comes, centuries before Chan. Laozi chapter 1 and chapter 11's emptiness are its ancestors; Zhaozhou's genius was compressing the whole doctrine into a sound a dog could answer to.
What kind of no is it, when the teacher forbids you to understand it as no?