Rochelle Inselman’s obsession has haunted Minnesota’s debate over gun violence this year.

She was denied a permit to purchase a weapon by her hometown police department in Eden Valley, south of St. Cloud, because background checks turned up a history of violating restraining orders. She went on an Internet site and arranged for the private purchase of a 9-millimeter handgun and ammunition.

The sale required no background check.

On Feb. 12, 2012, she went to the home of an ex-boyfriend, Bret Struck, in Brooklyn Center, whom she had stalked for eight years. She killed him, firing every round that came with the gun, and is now in prison for 40 years.

Kevin Benner, chief of the Brooklyn Center Police Department, which investigated Struck’s murder, has used the Inselman case to argue in favor of universal background checks — extending the background checks now in place for purchases from licensed firearms dealers to all private purchases of handguns and semiautomatic, military-style assault rifles.

The issue, which is expected to come to a vote in the Minnesota Senate Judiciary Committee on Thursday night, is a big part of the national gun debate in the wake of the Newtown school massacre in December. In Minnesota and at other state Capitols, the two sides are contesting how big a loophole exists in the current system and whether people intent on doing harm would be deterred by a background check.

Chris Rager, lobbyist for the National Rifle Association in Minnesota, says such a change would end traditional neighbor-to-neighbor transactions without stopping those as intent on violence as Inselman.

“Universal background checks aren’t universal,” Rager told the Legislature. “Criminals won’t submit to these background checks.”

In Minnesota this legislative session, discussions have included banning assault weapons or high-capacity magazines, allowing local police to look deeper into the mental health histories of people applying for permits, and more severely punishing felons who illegally possess weapons. As weapons and ammunition bans have fallen by the wayside, universal checks have become a top priority for gun-control and police groups.

Dennis Flaherty, head of the Minnesota Police and Peace Officers Association, which is leading the charge for the bill, calls universal background checks “the public safety bill of the session.”

Bills pending in the House and Senate would require private sales of handguns and semiautomatics to go through a licensed dealer, who would conduct background checks for the private parties and could charge a fee. The idea has widespread support — 72 percent in a Star Tribune Minnesota Poll conducted last month, including 60 percent support from gun owners.

The current system for conducting background checks for firearms purchases is an inexact science, performed both by licensed private firearms dealers and by local police and sheriff’s departments. No one is perfectly satisfied with the current system, which has information gaps and can put local officials in a no-win situation.

“How do you know when someone’s going to snap?” said Ernest Junker, chief of the Eden Valley police department, which denied Inselman her permit to purchase. “Those things are hard to control.”

According to Kevin Vick, an NRA supporter and licensed firearms dealer in Lakeville, dealers perform background checks on buyers of all guns, including handguns, semiautomatics and traditional hunting weapons, using the federal National Instant Criminal Background Checks System. Vick said there are “big holes” in information reporting by the states, and he supports efforts to improve it.

In Minnesota, buyers of two classes of weapons from dealers — handguns and semiautomatic, military-style rifles — must also obtain permits from local law enforcement authorities.

Brooklyn Park Police Sgt. Mark Bergeron, who reviews permit-to-purchase requests for his department, said applicants’ names are run through various databases — the FBI’s National Crime Information Center, Minnesota’s court system, the federal instant checks system, Brooklyn Park records, lists of predatory offenders and state records of those who have been committed as mentally ill.

Most come back with nary a blemish and the permits are issued, Bergeron said. Some show arrests that require further investigation, he said, but most of those are not disqualifying convictions. He estimates denying about 8 to 10 percent of applications, which have been on an upward slope lately, from 394 in 2006 to 899 in 2012.

He described the case of an applicant who had attempted suicide three months earlier and had told a friend if she had a gun she would take her own life. Now she wanted to buy a gun, and because she had not been judicially committed as mentally ill, she may have met the technicalities of the law. He denied the permit.

“I can’t in good faith give that person a permit,” he said.

The current checks apply when licensed dealers are making sales, whether in their shops or at gun shows. They do not apply to person-to-person transactions, whether at gun shows, over the Internet or across the backyard fence. The proposed bills would close this loophole.

“We would submit that it’s not really a loophole, but a huge gaping hole that allows as many as 40 percent of the gun transactions in our state to take place through private sales,” said Flaherty, the police association’s leader. “It is the route that people who know that they are ineligible to pass a background check will travel.”

The 40 percent figure has come under attack. Vick and the NRA say that is an old estimate, produced before federal background checks began. Two professors who produced the estimate, Philip Cook of Duke University and Jens Ludwig of the University of Chicago, say it was based on gun surveys that no longer exist, and they do not know the current number.

Vick estimated that “98 percent” of guns sold at gun shows go through dealers with federal background checks, as do interstate gun sales arranged over websites. He said a universal background check law is aimed at the wrong people, imposing a new burden on “10 percent of law-abiding citizens.”

The chances for universal background checks remain iffy. A competing bill supported by the NRA, which focuses on improving background-check information and cracking down on “straw purchases” of guns by intermediaries, appears to have more support.

Supporters remain convinced that this is a vital step. “We’re not talking about banning any guns,” said David Chipman, a former firearms agent who has lobbied the Legislature on behalf of a national group, Mayors Against Illegal Guns. “We’re going to say, at worst, you’re going to be mildly inconvenienced for the sake of public safety.”