Jared Walczak, the vice president for state projects at the Tax Foundation’s Center for State Tax Policy, said that the fine print in the law raised many complicated questions for states that, in some cases, would be awarded money for things that they either do not need or that they already had plans to pay for out of their budgets. It is not clear, for example, if a state could use aid money for an expense related to the coronavirus that it was already planning to pay for and then offer tax credits with the additional surplus.

“If the federal government intends to forbid any sort of revenue negative tax policy, no matter what its size, because a state received some funding, that would be a radical federal entanglement in state fiscal policy that may go beyond what was intended,” Mr. Walczak said.

Such questions will largely hinge on how Treasury Secretary Janet L. Yellen interprets the legislation and what guidance the Treasury Department gives to states.

A department official noted that the law says that states and territories that receive the aid cannot use the funds to offset a reduction in net tax revenue as a result of tax cuts because the money is intended to be used to support the public health response and avoid layoffs and cuts to public services. More guidance on the matter is coming, the official said.

The lack of clarity also raises the risk that states use the money for projects or programs that do not actually qualify under the law and then are forced to repay the federal government. States are required to submit regular reports to the Treasury Department accounting for how the funds are being spent and to show any other changes that they have made to their tax codes. The department will also be setting up a system of monitoring how the funds are being used.

Emily Swenson Brock, the director of the Federal Liaison Center at the Government Finance Officers Association, said that the eligible uses of the federal aid appeared to be relatively limited for the states and that some might actually find it challenging to deploy the money in a useful way.

“It’s complicated here for the states,” Ms. Brock said, adding that her organization had asked the Treasury Department for an explanation. “Congress is reaching in and telling these states how they can and can’t use that money.”

Before they receive federal funds, states will have to submit a certification promising to use the money according to the law. They could also decline funding or, if they are set on tax cuts, they could offset them with other sources of revenue that do not include the federal funds.

For many states, the federal money is welcome even if they do not necessarily need it for public health purposes.

Melissa Hortman, the speaker of the Minnesota House of Representatives, said that she was hopeful that the federal government gives states the flexibility to use the money to make up for lost revenue from the virus. She suggested that the state should look to make new investments in education and transportation. Minnesota is expected to have a budget surplus for the next two years and will receive more than $2 billion in aid.

“It’s not too much money,” said Ms. Hortman, a Democrat. “Our country has just lived through a once-in-a-hundred-year pandemic.”

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