Californians might agree there’s a housing crisis, but they’re split widely on how to tackle it, according to a poll released Tuesday by UC Berkeley.

Slightly more than half of residents say the state needs to exert more control over local development decisions to address the deepening housing shortage, a survey by the Berkeley Institute of Governmental Studies found. However, 47 percent of Californians disagree. Bay Area residents favored more state involvement by a 14 percent margin, 56 to 42 percent.

“It’s an almost even split,” said Mark DiCamillo, director of Berkeley IGS. “This is something that strikes a political nerve. It stirs passions.”

The divided public opinion mirrors a similar divide in the state legislature in Sacramento. Efforts to increase state control over local development have stalled for two years, including an ambitious overhaul of housing policy proposed by Sen. Scott Wiener, D-San Francisco. The measure, SB50, would have forced cities to build more housing and allowed denser development along busy transit routes.

California has a housing deficit of 3.5 million units, state planners estimate, as cities have largely ignored and fallen short of meeting state guidelines for producing new housing. Median home prices in the Bay Area have increased almost uninterrupted, year-over-year, since April 2012 and made the region one of the nation’s most expensive places to live.

More than 8 in 10 Bay Area residents cited housing costs as a very or extremely serious problem, according to a poll conducted this year for the Silicon Valley Leadership Group and this news organization.

Russell Hancock, CEO of Joint Venture Silicon Valley, believes Bay Area residents have become more open to new solutions to the housing shortage in the last five years.

Hancock said the Berkeley poll reflected a shift in attitudes by Valley residents toward a bigger role by Sacramento in city and county development decisions. “It’s better than I might have thought,” he said. “It’s suggesting that people in the Bay Area are now beginning to feel this is epic — a full-blown crisis.”

The poll also found diverse opinions about how to solve the shortage — through more subsidies, developing denser housing around transit, expanding rent control, or another solution.

About one-third of residents think the state should offer additional housing subsidies to low- and moderate-income homebuyers, while one-quarter favor more multi-family development and 17 percent say more rent control should be approved. Another 24 percent said none of those options would solve the problem.

In the Bay Area, residents preferred more apartments along rail and bus lines with 33 percent in favor than subsidies (26 percent) and rent control (17 percent).

Younger residents and renters were most likely to embrace state control, while older residents, homeowners and conservative voters preferred local officials deciding growth in their cities.

California voters largely agree on one question: three in four said the state should impose limits on new housing in areas with the highest risk of wildfires. “The concept is broadly supported,” DiCamillo said, adding that the question did not mention specific regions.

Roughly 1 in 4 California residents live in areas potentially at a high risk of wildfires, according to a state report.

Hancock said after years of slow-growth decisions by local planning commissions and city councils, Bay Area residents are looking for other solutions. “Regular folks out here realize the market’s not fixing the problem.”

Tech companies are stepping up, too, he noted, with Google’s announcement Tuesday to invest $1 billion in Bay Area housing.

“It’s breathtaking. It’s staggering and amazing,” Hancock said. “This can be a game-changer.”

The IGS poll surveyed 4,435 registered voters online, in Spanish and English, between June 4 and 10. It has an expected sampling error of plus or minus 2.5 percentage points.