ST. PAUL  — State tax officials in Minnesota and Wisconsin said they’re working to reinstate a system that allowed 80,000 people who work across their shared border to file one state income tax return.

Under the reciprocity system that began in 1968, Wisconsin made payments to Minnesota to make up for what border-crossing Wisconsin residents would have given to Minnesota in taxes. More people live in Wisconsin and work in Minnesota than vice versa.

The system was stopped in 2009 by former Minnesota Gov. Tim Pawlenty because the state was losing money. Wisconsin was 15 months behind on payments, and there was disagreement on how much was owed.

The states’ governors want a new agreement as long as it’s fair, according to Minnesota Revenue Commissioner Cynthia Bauerly and Wisconsin Secretary of Revenue Richard Chandler.

“We’ve been working to do that,” Chandler said. “We think this would be beneficial to taxpayers in both states.”

Minnesota would get $90 million to $100 million a year if the agreement were still in place, the Minnesota Department of Revenue says.

A bill introduced in the Minnesota House would lift a sticking point between the two states that remains after a series of reconciliation attempts. It would essentially drop a claim that $5 million more should go to Minnesota to cover a difference in tax breaks.

Minnesota Rep. Greg Davids, R-Preston, said the bill is a “work in progress.” Leaders in Wisconsin support it, but Minnesota Gov. Mark Dayton’s administration hasn’t backed it. Bauerly said she wants to work with Davids on the bill.

Any changes would have to wait until at least next year’s state income tax returns. Wisconsin Sen. Sheila Harsdorf, R-River Falls, said she’s heard complaints from constituents since the agreement was halted.

“It continues to be a tremendous frustration,” Harsdorf said. “Not only is it a hassle, but it’s a lot more costly. … No one is going to fill out two tax returns for the price of one.”