Well, since I've been shopping Lunds - a Twin Cities chain of grocery stores - for more than 15 years, I believe I have only ever bought one variety of garlic. You know, softneck grocery store garlic (either California Early or California Late - the two most popular commercial varieties). And since softneck garlic can only be grown successfully in much warmer climes than Minnesota (mostly California), there's no way that softneck garlic is local.
But on Saturday the big garlic bins at Lunds held these nice, purple, somewhat-smaller-than-usual hardneck bulbs. There was no mention of them being a different type, the price was the same as it's always been, but these were definitely hardneck garlic bulbs. (FYI - the thick, hard stalk in the middle of the head was the dead giveaway. Softneck garlic is all cloves, hardneck still has the stalk in the middle.)
So were they local? I don't really know for sure, but Lunds has really been pushing (and marketing) their local and organic products for the past few years, so I wouldn't be shocked if this garlic was from somewhere in the Midwest. And I think that's kind of cool - the idea that "buying local" was so not-a-big-deal that they just do it when the produce is in season and don't even make a fuss about it.