CONCORD, N.H. — As some states look to tobacco tax increases to plug budget holes, a few are bucking the national trend and saying, “If you smoke ’em, we got ’em,” looking at dropping the rate to boost cigarette sales.

In New Hampshire, supporters argue that reducing the tax by a dime would help the state compete with Maine, Vermont and Massachusetts, while opponents say it would still lose millions of dollars even if higher sales resulted.

New Hampshire’s House voted Thursday to reduce the tax and sent the bill to the Senate, where its prospects are uncertain. New Jersey and Rhode Island have also considered reducing their taxes.

Aaron Evans, 25, weighed his potential new option Thursday as he stopped at a convenience store in Haverhill, Mass, for a sandwich and a $7.13 pack of Marlboro cigarettes. A pack would cost him $5.99 a couple miles away in New Hampshire, which already has significantly lower taxes than Massachusetts.

He welcomed any move to make smokes cheaper but said a dime a pack wouldn’t make him change his buying habits.

“You’ve got to average it out,” he said. “I could either drive all the way over to New Hampshire and waste the gas — it kind of evens it out.”

It’s very unusual for states to lower the tax, said Frank Chaloupka, an economics professor at the University of Illinois at Chicago. The sales increase isn’t enough to offset the drop in tax revenue, he said.

States have enacted 100 increases over the past decade, he said.

New Hampshire raised its tax repeatedly since Democratic Gov. John Lynch took office in 2006, increasing it from 52 cents per pack in 2005 to $1.78 currently.

“New Hampshire has been going in the same direction as the rest of the country, basically forever,” Chaloupka said.

The bill passed by the House would cut the rate 10 cents to $1.68 per pack. The taxes are $2.51 in neighboring Massachusetts, $2 in Maine and $2.24 in Vermont.

Rhode Island’s bill would cut its tax by $1, to $2.46 per pack compared with $3 in neighboring Connecticut. New Jersey last year considered reducing its tax 30 cents, to $2.40 per pack, but hasn’t followed through. Across the river from New Jersey, smokers in New York City pay the nation’s highest cigarette tax, a combined state and local rate of $5.85 per pack.

When states raise the tax, revenue goes up even though sales decline, Chaloupka said. Over time, tobacco tax revenues gradually drop after a tax hike as smoking use declines, he said. To drive revenues back up, states have raised taxes again.

The only time tax revenues dropped after a state raised its tax was in 2006, when New Jersey raised its rate 17.5 cents, he said — though the revenue decline was more likely due to adoption of a comprehensive smoke-free policy.

New Jersey raised the tax 12.5 cents in 2009 and revenue rose, he noted.

Chaloupka asserted that any reduction in cigarette prices would add to Medicaid and other health care costs. The Campaign for Tobacco-Free Kids estimates that if the New Hampshire cut is enacted it would mean more than $21 million in long-term health costs.

The campaign also estimates a 10-cent drop per pack would result in 1,000 new young smokers in New Hampshire.

New Hampshire has historically looked to export its tax burden — and any resulting health costs — to other states through taxes on products such as tobacco and alcohol it sells to its residents.

“That’s always been the way we run our tax structure,” said Mike Rollo, spokesman for the American Cancer Society in New Hampshire. “We’ve always tried to tax people from out of state.”

State Rep. Susan Almy, a Lebanon Democrat and member of the House Ways and Means Committee, said the health impact was not taken into account in the committee when it promoted the tax cut.

Instead, lawmakers are looking at a study by the New Hampshire Grocers Association, which has consistently criticized the tax increases as hurting small businesses, particularly along New Hampshire’s state line.

Grocers Association President John Dumais said Thursday its study shows that cutting the rate a dime would cost the state tobacco tax revenues but would be offset by an increase in state taxes collected from people renting hotel rooms, eating in restaurants, and buying alcohol, lottery tickets and gasoline.

The net result would be no loss of revenue to the state but an incentive for tourists to visit the state to shop, he said.

“People coming from out of state are going to have an empty gas tank. They’re going to be hungry. They’re going to be tired,” he said. “It’s going to help every business.”

State Rep. Patrick Abrami, R-Stratham, made that argument successfully during the House debate.

“We have reached the tipping point,” he said. “We are hurting our merchants. We are losing sales on our borders.”

But state Rep. Christine Hamm, a Hopkinton Democrat, called the move “fiscally stupid.”

“No state has cut their tobacco tax and seen a revenue increase,” she said.

New Hampshire Senate Finance Chairman Chuck Morse said he believes the Senate will support the cut.

“I think it’s a positive sign for business. I think it will provide revenue in the long run,” said Morse, a Republican who lives in Salem.

Unlike in other states where campaign contributions have the potential to sway votes, New Hampshire House members are unpaid volunteers and spend very little on campaigns — so it’s unlikely that tobacco money is essentially paying for votes.

But lobbying organizations do target the smaller Senate because it’s easier to win votes, and the potential benefit to tobacco companies remains clear.

“Yes, we do support the excise tax rollback as it would benefit retailers, consumers, jobs and bring tobacco tax revenue back to New Hampshire,” said David Sutton, a spokesman for Altria Group, the parent company of Phillip Morris USA Inc.

If approved by the Senate, the cigarette tax cut bill would go to the governor, who doesn’t support it. But the House and Senate, led by Republicans, could override a veto by the governor, saving cigarette smokers 10 cents a pack.

The House voted 236-93 to send the bill to the Senate anyway. Pro-business Republicans who control the Legislature are siding with Dumais’ argument that the ripple effects from cutting the rate make it worth doing.

Lynch spokesman Colin Manning, who said the governor doesn’t support the tax cut, pointed out that New Hampshire’s tax rate already is the lowest in the region.

Unlike the other states, New Hampshire has no sales tax.

Manning said the House is considering making much deeper budget cuts than Lynch proposed “and now with this action today it raises the question of what else they are going to cut.”