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CHICAGO — The federal government is threatening to withhold about $87 million in food stamp funds from the state of Illinois if Cook County doesn’t alter the manner in which the penny-an-ounce tax on sweetened beverages has been implemented, officials said Thursday.

The U.S. Department of Agriculture is objecting to how the tax is applied to purchases using food stamps, known as the Supplemental Nutrition Assistance Program. It says the county must take “immediate steps” to become compliant, adding no taxes can be collected until the problem is solved.

Cook County officials told retailers that purchases made with food stamp benefits are exempt from the soda tax under federal law. However, it allows retailers to tax those purchases and provide refunds as a workaround for stores that haven’t been able to properly update their point-of-sale systems.

The Agriculture Department on Monday warned the Illinois Department of Human Services in a letter that the refund system violates federal law and money could be withheld.

“It is (Food and Nutrition Services’) strict interpretation that retailers may not charge the tax to SNAP recipients at any time and that providing an immediate subsequent refund at a customer service desk does not cure the problem or the violation of the law,” said DHS official James Dimas in a memo to Cook County President Toni Preckwinkle on Wednesday.

A spokesperson for Cook County Board President Toni Preckwinkle said they do not believe the tax violates SNAP rules. They said the board spoke with the USDA on June 27 while drafting the legislation, and did not hear back from the agency regarding any issues.

“If we were specifically told that the Regulation 2017-3 was unacceptable, we would have worked with USDA, just as we had been doing since January, to further modify as needed,” the statement said. “We do however recognize that USDA’s powers against the State in this regard are substantial and we will work collaboratively with both the State and USDA to address USDA’s concerns.”

The penny-per-ounce tax imposed by Cook County went into effect last week. It was originally slated to begin July 1, but was delayed by a lawsuit filed by the Illinois Retail Merchants Association that was later dismissed by a Cook County judge. The merchants are appealing the judge’s decision.

Under the sweetened beverage tax, drinks in a bottle, or from a fountain machine, are taxable. But on-demand, custom-sweetened beverages, such as those mixed by a server aren’t subject to the tax.