* Follows other moves in Europe to reduce nuclear reliance
* Row over law focuses on cost to customers, taxpayers
* Critics say measures could push up power imports
* Polls so far suggest law will pass, but support falls
By John Miller and Rupert Pretterklieber
ZURICH, May 17 (Reuters) - Swiss voters will on Sunday determine the fate of a law proposing billions of dollars in subsidies for renewable energy, a ban on new nuclear plants and a partial utilities bailout.
Polling so far suggests the law will be approved in the binding referendum, but support has slipped. A survey this month by research institute gfs.bern for state broadcaster SRG showed 56 percent of voters backed the law, down from 61 percent.
The Swiss initiative mirrors efforts elsewhere in Europe to reduce dependence on nuclear power, partly sparked by Japan's Fukushima disaster in 2011. Neighbouring Germany aims to phase out nuclear power by 2022. Nearby Austria banned it decades ago.
Debate on Switzerland's "Energy Strategy 2050" has focused on what customers and taxpayers will pay for the measures and whether a four-fold rise in solar and wind power by 2035, as envisaged in the law, can deliver reliable supplies.
Critics say a family of four would pay 3,200 Swiss francs ($3,257) in extra annual costs and say more intermittent wind and solar energy would mean a greater reliance on imported electricity. Switzerland was a net power importer in 2016.
"This law will lead to massive increases to the price of energy while leaving Switzerland without adequate, reliable power," said Toni Brunner, leader of the opposition Swiss People's Party (SVP) which helped force the referendum.
Opposition posters show a woman shivering under a cold shower, suggesting this is what voters face if they say "yes".
Energy Minister Doris Leuthard, whose government proposed the law, dismisses opposition estimates as highly inflated. She said the package would cost the average family 40 francs more a year, based on a higher grid surcharge to fund renewable subsidies.
"The SVP is including costs related to a second phase of the Energy Strategy that is not up for a vote," she said in a television interview.
The price tag row largely hinges on whether costs are based on the surcharge alone or also include future expenses related to managing the reduction of fossil fuel use and emissions. The SVP puts the broader costs at about 200 billion francs.
The law would raise 480 million francs a year from electricity users to fund investment in wind, solar and hydro power, while 450 million francs would be earmarked from an existing fossil fuels tax to help cut energy use in buildings by 43 percent by 2035 compared to 2000 levels.
Solar and wind now account for under 5 percent of output, compared with 60 percent for hydro and 35 percent for nuclear. Under the law, power from solar, wind, biomass and geothermal sources would rise to at least 11,400 gigawatt hours (GWh) by 2035 from 2,831 GWh now.
Swissmem, the electrical and mechanical engineering industry lobby, has urged a "no" vote, citing the variability of renewable supply. "Even limited interruptions in our electricity supply can cause massive costs," said spokesman Ivo Zimmermann.
The law will ban building new nuclear plants. Switzerland has five plants, with the first slated to close in 2019. Voters have not set a firm deadline for the rest, allowing them run as long as they meet safety standards.
Supporters say the law would help utilities which rely on hydropower, whose costs exceed Europe's wholesale prices.
Alpiq, BKW, AXPO and other utilities would share a 120 million franc annual subsidy to help close the gap between production costs and market prices. Other funds would help build new dams or refurbish old ones.
About 38,000 renewable projects, mostly small roof-top solar installations, await approval as a national fund to support them has insufficient funds. Supporters say the new law would help end the logjam. ($1 = 0.9824 Swiss francs)
Editing by Nina Chestney and Edmund Blair