Despite predictions that right-wing money would flood the political system after the Supreme Court threw out key campaign finance laws, a survey finds that left-leaning groups, led by labor unions, outspent conservative donors like the billionaire Koch brothers in state political advertising wars last year.

Outside groups — nonprofits, super PACs, business and labor groups, and private individuals — spent at least $209 million to influence state-level elections in the 38 states in the 2012 election cycle. Money funneled through party groups such as the Democratic Governors Association and Republican Governors Association accounted for nearly 40 percent of the $209 million.

The study, released this week by the watchdog group the Center for Public Integrity, also found that groups supportive of Democrats, led by labor unions, outpaced their GOP rivals by more than $8 million in those states, spending some $44 million to aid Democratic campaigns.

The findings were based on an analysis of data compiled by the National Institute on Money in State Politics and state elections offices. It focused on the states that had significant gubernatorial and state legislative races last year and had data on campaign giving.

The findings challenge the popular narrative that business groups and big donors like the industrialist brothers David and Charles Koch would give conservative candidates a major financial leg up in the wake of the Supreme Court’s Citizens United ruling in 2010 that lifted many of the long-standing limits on corporate and union campaign spending, while effectively invalidating some two dozen state laws on independent spending by outside groups.

“The narrative has been that Citizens United is just going to help corporations, and people have forgotten that you can take unlimited union money too,” said John Dunbar, managing editor for politics at the Center for Public Integrity.

Political ads in states often are purchased by the Republican Governors Association or the Democratic Governors Association with undisclosed contributions. The CPI survey said heavy outside money appeared to have clear effects on races in New Hampshire, Maine, Colorado and other states.

“It’s disturbing that somebody out of state is getting involved in your state election pouring millions of dollars into the state election and you have no idea where that money is coming from,” Mr. Dunbar said. “As a voter, that’s not exactly an informed decision.”

The Republican Governors Association, with at least $34 million, was the largest single outside spender in the states surveyed in the report.

Conservative individual donors were also active: Hedge fund billionaire Paul Singer gave the Republican Governors Association $1.25 million, and David Koch gave $1 million.

The Republican State Leadership Committee, sometimes known as the association’s “little brother,” received $1.2 million from the Koch-backed super PAC, the American Future Fund. Outside conservative money was credited with helping Republicans wrest the North Carolina and Arkansas state legislatures from Democratic control.

Analysts say one reason for the heavy state giving patterns is that the money can have far more of a policy impact at the state level than in national campaigns.

“Republicans have said they have given up on the gridlocked Congress and that they can do better at the state level, but it’s actually the Democrats doing better at the state level,” Mr. Dunbar said.

In New Hampshire, for example, Republican gubernatorial candidate Ovide Lamontange emerged from the primaries last year with a $250,000 to $17,000 cash-on-hand advantage over Democratic rival Maggie Hassan.

The advantage might have proved decisive, but Ms. Hassan triumphed in part with the help of out-of-state groups spending millions of dollars to attack the Republican nominee.

The Democratic Governors Association spent roughly $7 million on ads bashing Mr. Lamontagne, who backed right-to-work legislation that labor unions say undercuts their bargaining power in organizing workplaces. In the end, outside groups on the left and right spent a total of $18 million on New Hampshire gubernatorial and state legislative races — $5 million more than the state’s candidates reported raising themselves.

“Hassan was propped up and carried to victory by the outside groups, ” said Fergus Cullen, a former head of the New Hampshire state Republican Party, who helped raise funds for Mr. Lamontagne.

The Center for Public Integrity also found that the majority of the money pouring in from these outside organizations was channeled to out-of-state advertising agencies as well. The biggest winner last year was California-based Target Enterprises, which earned more than $18.8 million from Republican national groups for creating conservative ads for state elections. Democratic advertising firm GMMB/Great American Media/Waterfront Strategies, based in Washington, D.C., came in second, earning more than $17 million in business.

This year’s election campaigns also were funded primarily by out-of-state organizations. According to the New Jersey Election Law Enforcement Commission, at least $35 million was spent by outside groups on the gubernatorial and legislative races in which Republican Chris Christie was re-elected governor and Democrat Cory A. Booker was elected to the Senate.

In Virginia’s gubernatorial race, the Republican Governors Association was the single largest donor to Kenneth T. Cuccinelli II, and the Democratic Governors Association was the top donor to the winning candidate, Terry McAuliffe.

The influence of outside spending groups like the governors associations is projected to be even greater next year, when 36 governorships are at stake.

“There’s no question that we will see a huge impact of this in the next elections,” said Mr. Dunbar. “When we had races in 2010, the Citizens United decision was still fresh and people were still trying to figure out how to take advantage of it. Now people know how to use it.”

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