TOMAH, Wis.—Farmers markets, with their hodgepodge of organic kale, artisan rye bread and peach preserves, have surged in popularity in recent years. But now authorities are questioning whether they're missing a crucial ingredient: real farmers.

Here in Tomah, where a farmers market has operated for the past decade in a grassy downtown park, a nasty dispute has cropped up. Local farmer Ronald Waege, who grows his own apples and blueberries just outside of town, says resellers are buying up produce at an auction and peddling...