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AUGUSTA, Maine — Maine has set aside $35 million of the $1.25 billion in coronavirus relief money under a federal stimulus for local and tribal governments, but it can only be used to cover municipal costs under a matching program and not to help struggling businesses.

Under a Federal Emergency Management Agency program, the federal government will reimburse 75 percent of costs incurred by municipal governments in their virus response if state and local governments contribute 25 percent, according to a Tuesday release from Maine’s budget department.

That will give cities and towns more to work with, but it will also restrict some of the ways they can use the federal money. Emergency medical care, personal protective equipment and overtime costs for government employees would be covered, but state and local governments cannot use FEMA money to offset business losses.

Since Maine received the CARES Act funding in May, Gov. Janet Mills, a Democrat, has faced criticism from some mayors, who argued that the state needed to quickly release money to cash-strapped cities and towns.

Auburn Mayor Jason Levesque, a Republican who has been one of Mills’ most vocal critics on the issue, said Tuesday he was encouraged to see the state start to distribute the money, but that spending money matched through FEMA grants may not meet the greatest need.

“It’s still tying our municipal hands, so we are not as effective as we can be in providing direct business relief,” Levesque said.

Some industry groups have argued that Maine should use a significant portion of its CARES Act funding to prop up businesses that have been hurt by the virus restrictions. New Hampshire designated the plurality of its CARES Act money for a business relief program.

So far, Maine has also designated CARES Act money to backfill the state’s strained unemployment trust fund. Neither the stimulus funds nor the FEMA grant money can be used to backfill budget shortages due to declines in tax revenue.

In a Tuesday news release, Mills reiterated her call for more assistance from the federal government to reduce that strain, plus “more flexibility” so the state can be more helpful to municipalities going forward.