CHICAGO (Reuters) - The failure of three U.S. states to enact legislation to fund education has left hundreds of school districts scrambling for cash as students return to the classroom.

Connecticut, Illinois and Wisconsin began fiscal 2018 on July 1, but lawmakers have been unable to pass an overall budget or a way to distribute budgeted money to schools, which depend on local property taxes and state dollars for their operations.

A political dispute over a new school funding formula is holding up $6.7 billion in state aid for Illinois' 852 districts.

Moody's Investors Service warned on Thursday that as many as 20 of the 256 school districts it rates in Illinois face credit deterioration in the coming months by tapping reserves or borrowing to make up for state aid.

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The credit rating agency already has the Chicago Public Schools (CPS) under review for a potential downgrade deeper into junk due to the uncertainty of state funding.

Republican Governor Bruce Rauner used his veto to rewrite a funding formula bill passed by the Democratic-controlled legislature, removing additional money allocated to CPS, the nation's third-largest public school system. The amendatory veto was overturned by the Senate on Sunday. The fate of next week's veto override vote in the House was uncertain.

Deliberations over Wisconsin's new two-year budget have been sidelined by legislation for a $3 billion incentive package for a proposed factory by Taiwan's Foxconn. State Assembly Minority Leader Peter Barca, a Democrat, questioned on Thursday why school funding was not a priority for the Republican-controlled legislature.

"We're six weeks late on a budget," he said during debate on the Foxconn bill. "I read yesterday that school districts are starting with substitute teachers because of the fact you have not fulfilled your obligation."

A budget needs to be in place by early October to calculate state-aid payments to Wisconsin's 422 districts, which use that information to set their property tax levies by a Nov. 1 deadline.

Governor Scott Walker proposed a $649 million boost for the fiscal 2018-2019 biennium, bringing total school funding to $11.5 billion.

Connecticut's budget stalemate has the state's 157 school districts on edge. Fran Rabinowitz, executive director of the Connecticut Association of Public School Superintendents, said how much state money will be allocated to schools is "completely up in the air," forcing some districts to eliminate jobs or put positions on hold.

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"This is just a very, very difficult way to start a school year," she said in an interview.

(Additional reporting by Suzannah Gonzales in Chicago; Editing by Matthew Lewis)