It is an allen hex head, the outside circumference is round, look closely, unless Berning changed it but I doubt that. A 3/32" works, I checked it, try it or if you are in Europe, buy a metric set. A corresponding size will be adequate or to be exact simply e-mail David Berning directly from his site.
My screws are Allen screws and my unit was the last ZH270 model David Berning made and he built it with all of his latest upgrades. Assuming your ZH270 is recent vintage, I would assume the screws are Allen screws. If your unit is pre-owned, some goofball could have rounded-off the inside of the screw.
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