Playing duffie lassie?

I remember when I was in Edinburgh my English teacher taught me an expression that was supposed to be Scottish. It was something like play the duffie lassie which should mean "that a girl plays dumb".

Anyway, I have Google around but cannot find it. Does this expression exist? At least, in Scotland?

Alexander Warrack & William Grant, Chambers Scots Dictionary (1911) has these entries for duffie and duffy:

Duffie, adj. blunt, round-pointed.

Duffie, adj. soft, spongy; foolish; cowardly. Cf. Doughy.

Duffy, adj. powdery, used of coal that crumbles when struck by the poker; soft, spongy; stupid.—n. a soft, silly fellow.

The cross-referenced word doughy has this entry:

Doughy, adj. half-baked; 'soft'; foolish; cowardly. Cf. Daighie.

And for daighie, Chambers has this:

Daighie, adj. doughy; soft, flabby; spiritless; cowardly; childish; ill-dressed; used of rich ground: composed of clay and sand properly mixed.

A Google Books search for "duffie lassie," "duffy lassie," "duffie lass," and "duffy lass" yields no meaningful matches, suggesting either that you misheard the words or that the expression has left virtually no footprint in published writings in the Google Books database. Still, the second definition of duffie and the first (and only) of duffy in Chambers (above) appear to match the meaning of "duffie lassie" that your teacher in Edinburgh gave you. So perhaps a "duffie [or duffy] lassie" is indeed a girl who behaves in a soft, spongy, foolish [or stupid] way, whether she really is so or is simply playing a part.