SALT LAKE CITY — Utah voters will decide Tuesday whether to adopt the country's first statewide school-voucher program that would be open to anyone. The referendum could influence efforts elsewhere to use tax dollars for private-school tuition.

Utah's voucher law would grant $500 to $3,000, depending on family income, for each child sent to private school. Unlike other voucher plans geared toward low-income students or those in failing schools, Utah's plan would be available to anyone, even affluent families in well-performing districts.

It's one of several noteworthy ballot measures confronting voters in six states in the off-year election. Topics include stem-cell research in New Jersey, gambling in Maine and a hefty cigarette tax increase in Oregon to fund health insurance for children.

Utah's hotly disputed voucher law won approval by one vote in the Republican-controlled Legislature in February. The law was suspended before taking effect when opponents gathered more than 120,000 signatures to force an up-or-down referendum vote.

"It's unusual for someone to say 'As goes Utah, so goes the nation.' But this is a huge national issue," said Kim Campbell, president of the state's teachers union, the Utah Education Association, which opposes the measure.

Supporters of vouchers say the program would reduce crowding in public schools and give parents more choices. Children already in private schools would not qualify.

Critics say the money would be better spent in public schools. Utah spent less per student — $5,257 — than any other state in 2005, according to the Census Bureau. And the school system must deal with the state's highest-in-the-nation birth rate.

Among noteworthy ballot items elsewhere:

• In Oregon, a measure to raise the cigarette tax by 84.5 cents a pack — to $2.02 — to pay for health insurance for about 100,000 children now lacking coverage. Tobacco companies opposing the measure have outspent supporters by a 4-1 ratio, contributing nearly $12 million. The campaign has, in many ways, mirrored the debate in Congress over the Democrats' vetoed proposal to boost spending on children's health care.

• In New Jersey, a measure authorizing the state to borrow $450 million over 10 years to finance stem-cell research. The Roman Catholic Church and anti-abortion groups oppose the measure, which was placed on the ballot by the Legislature with strong backing from Gov. Jon Corzine.

• In Texas, a proposal to create a cancer-research institute and authorize up to $3 billion in bonds over 10 years to finance it.

• In Maine, a measure that would allow the Passamaquoddy Indians to operate a racetrack casino with up to 1,500 slot machines in the hard-up town of Calais.