WASHINGTON — Local school districts face renewed budget pressure as states cut back spending, forcing local governments to weigh tax increases and layoffs, the Center on Budget Policy Priorities said in a recent report.

Meanwhile, some municipal bond investors are delving deeper into a school district’s credit supports, scrutinizing students’ test scores, free-lunch programs, and the legal requirements needed to raise taxes — all in an effort to judge an issuer’s ability to pay bondholders, sources said.

The CBPP report said the fiscal austerity themes playing out in Washington and state capitals are filtering down the governmental grapevine.

The report found 21 of 24 states analyzed are providing less per student to local school districts this school year compared to 2010-11.

In 10 states, the per-student funding level is down by more than 10%. Three of the states ­— South Carolina, Arizona and California — have cut local education aid by more than 20%.

“These numbers really make evident just how deep the cuts have been to K-12 education,” said Phil Oliff, a CBPP policy analyst and co-author of the report.

The cuts also “have a negative impact on the broader economy,” as teachers are laid off and the quality of education is reduced, he said.

The report noted that school districts rely heavily on state aid for funding. Generally, about half of a district’s spending comes from the state, though it varies from state to state, the report said. During the recession, the American Recovery and Reinvestment Act of 2009 provided $39 billion to K-12 and higher education funding, but those dollars have almost all been exhausted.

As the funding spigot is tightened from above, local governments are finding fewer options to generate revenue of their own. With property values still down as a result of the downturn, local governments are finding economic and political challenges to imposing tax increases, according to the report.

“Property values have dropped precipitously,” Oliff said. “These very large cuts to state funding leave school districts with very few alternatives for preserving educational services.”

Politically, tax hikes have been difficult to pass in many states. Oliff said the recent budget-writing processes focused too much on educational spending cuts, rather than a more balanced approach of cuts and tax increases.

“Far too many states relied solely on cuts when balancing their budgets,” he said.

States and their school districts are evaluating how to cope with the spending cuts, struggling to balance strong school services while keeping property taxes low.

The Chicago Board of Education last month raised property taxes by 2.1% to raise an additional $153 million for the city’s public schools.

Two of Utah’s largest school districts raised property taxes by 6% and 9% to compensate for losses in state funding and growing student enrollments.

But in New York’s budget earlier this year, school districts’ tax increases will be capped at 2% or the inflation rate. The new state law says a school district cannot increase property taxes above the previous year.

Moody’s Investors Service said at the time that the constraints could cause districts to tap their reserve funds.

Voters in Eagle County, Colo.’s school district will be asked this November to approve a $6 million increase in property taxes.

Bond investors are seeking a deeper understanding of a school district’s local economic fundamentals. With federal and state aid being cut back, districts may need to rely more on their own tax bases, sources said.

The important indicators include a district’s test scores, the number of students receiving subsidized lunches, and the local foreclosure rate.

These statistics can reveal that “the tax base may not be the one you want to be invested in,” said Mary Talbutt-Glassberg, vice president and fixed-income portfolio manager for Davidson Trust Co. “You’ve got to look at anything that is going to demonstrate the demographics.”

She emphasized that investors also need to understand a district’s ability to raise taxes. If the district needs state approval to raise taxes, “then to me, that’s more like a limited” general obligation bond, Talbutt-Glassberg said.

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