Voters in at least four states approved ballot referendums last week that could negatively affect credit quality, while voters in at least three other states endorsed credit-strengthening measures, like larger rainy-day funds, rating agencies said in two recent reports.

Published by Moody’s Investors Service and Standard & Poor’s, the reports agreed that voters in four states — Arizona, California, Massachusetts, and Washington State — approved referendums that could pose revenue or credit challenges, the reports said.

Arizona’s referendum outcomes could be the most challenging, and the least expected by state lawmakers.

Arizonians dealt a blow to Gov. Jan Brewer by rejecting two referendums that would have transferred a total of $469 million to the state’s general fund, for “open space” purchases and children’s health programs, to help close the state’s $825 million fiscal 2011 budget deficit. The fiscal 2011 budget was passed assuming they would sign off on these referendums, according to the Moody’s report.

But the rejections “could worsen the state’s liquidity and budget challenges,” Standard & Poor’s said.

Moody’s noted that the rejections could impede Brewer’s attempts to cut taxes.

Arizona was already in credit trouble before the referendums. Moody’s downgraded it to Aa3 from Aa2 in July. Standard & Poor’s rates the state AA-minus with a negative outlook.

California voters, who traditionally vote on a long list of ballot referendums, approved three credit-related propositions — one that immediately opens a $1 billion hole in the fiscal 2011 budget by  forbidding the state from using fuel tax funds for debt service.

However, the budget assumes that it will conclude with a $1.3 billion surplus, Standard & Poor’s said. If the rest of the budget holds, then the surplus would be able to cover the effect of the ballot proposition, the rating agency said.

In a credit-positive vote, Californians approved a proposition to pass the budget with a simple majority, not the two-thirds majority that had delayed previous ­budgets.

However, a two-thirds majority is still required to raise taxes. And a separate referendum was approved that classifies various “fee” revenues as “taxes.” This referendum could impair future revenues now that the new “taxes,” formerly fees, need a supermajority to be approved, analysts said.

“In some ways, it’s back to where they were before,” said Standard & Poor’s analyst Gabriel Petek. “What was holding up the two-thirds vote on the budget was tax increases.”

Three states, Virginia, Oklahoma, and South Carolina, took positive credit actions by raising rainy-day fund contributions. Hawaii voters gave lawmakers the option to put budget surpluses into the rainy-day fund.

Washington voters rejected an income tax on high wage-earners and a previously approved tax increase on food and beverages. However, the lost revenue will likely “exacerbate budgetary pressures” without hurting credit quality, Standard & Poor’s said.

Massachusetts voters also shot down a previously approved tax, on alcohol. Moody’s said the loss of about $120 million is “manageable.”

Lynn Reaser, an economics professor at Point Loma Nazarene University in San Diego, said the California ballot measures “are unlikely to have a significant impact” on the state’s credit quality.

The policies of the state’s new governor, Democrat Jerry Brown, could have the largest impact on the state’s rating going forward, she said. Brown has proposed that all new tax increases need to be approved by voters.

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