While authorities search for details in the shooting deaths of two Brooklyn police officers at the hands of Ismaaiyl Brinsley, just hours after he shot his ex-girlfriend in the stomach, they know that he did not initially purchase the murder weapon.

Police say Brinsley used a semiautomatic Taurus handgun, bought in 1996 at a pawn shop in Atlanta by someone else, to kill the two officers before turning the gun on himself.

Authorities don’t yet know how the gun got into Brinsley’s hands. But federal law prohibits gun sales to felons. He would have been barred from legally purchasing a firearm, since he was convicted of felonies related to shoplifting in Ohio and firing a stolen gun in Georgia; he was also arrested more than a dozen times, though mostly for petty crimes, according to The New York Times.

But that Brinsley did not buy the murder weapon directly from a shop is not surprising, say criminologists.

Through something known as the private sale loophole, he could have purchased the firearm in the private market at a gun show or out of someone’s trunk. Private dealers don’t have to conduct background checks on prospective buyers, as licensed firearms dealers are required by federal law. Additionally, guns get stolen, are passed from person to person or are bought by straw purchasers, those who buy on behalf of others.

In a state like New York, with some of the toughest gun laws in the country, guns might come through the so-called iron pipeline, in which guns are bought in states with lax gun laws — often in the South — and taken North to sell at inflated prices. In 2013, New York City authorities seized more than 250 guns and arrested 19 people involved in a gun smuggling ring from North and South Carolina, the largest gun bust in history.

“Most guns go through a few separate owners,” said Sam Bieler, a research associate at the Urban Institute in Washington, D.C., which focuses on gun violence and crime mapping. “Sometimes guns are sold legally. Sometimes they’ll float around neighborhood social networks. Sometimes they’re traded. Guns will often take a circuitous route from when they’re legally purchased to the crime in which they’re used.”

He added, “The big challenge is that we don’t yet know a huge amount about where criminals get their guns from.”

While the U.S. Bureau of Alcohol, Tobacco and Firearms (ATF) tracks guns recovered from crimes that were bought legally by someone with a federal firearms license, there’s no way for the agency to know how guns have cycled through private dealers.

In 2000 the ATF investigated 1,012 original sellers of guns who had sold a majority of guns seized in crimes, and nearly half the sellers were not able to account for all their guns. The ATF discovered that those sellers were missing 13,271 guns and had made 700 sales to potential traffickers or people barred from buying guns.

Police can report a crime gun to eTrace, the ATF’s electronic gun tracing database, but in the many states that allow private gun sales, criminals can get access to guns sold online or on social networks, according to Jennifer Cicolani, an ATF spokeswoman.

About 67,000 guns were listed for sale online from private, unlicensed sellers as of September 2013, according to the San Francisco–based Law Center to Prevent Gun Violence.

“We don’t track that, because it’s not necessarily against federal law,” Cicolani said.

Such practices, though, don't fly in states with stricter gun laws, such as California, where private gun sales are banned, or New York, where even private sellers must conduct background checks on buyers. But it’s perfectly legal in other states, as long as the private dealer isn’t knowingly selling the gun to someone who is prohibited from buying it.

One thing that makes it difficult to break down gun circulation is the Tiahrt Amendment, a 2003 law that bars federal firearms tracing data from being revealed to anyone other than law enforcement or prosecutors involved in criminal investigations, criminologists say.

After Tiahrt was approved, academics and researchers were prohibited from accessing gun-tracing information without approval from law enforcement agencies, under the pretext that it could jeopardize investigations.

“You can’t analyze national data the way we once did,” said Glenn Pierce, a criminology professor and research scientist at Northeastern University. “The Tiahrt Amendment makes it very difficult to trace.”

In 1995, before the amendment, he analyzed ATF tracing data and found that just 1 percent of gun dealers were the original sellers of 57 percent of the guns seized in crimes. More recently, he co-authored a study published earlier this month in the journal Injury Prevention in which his team found that crime guns traced by the ATF from 2003 to 2006 tended to be older in the states with tougher gun laws, such as California, meaning that it took longer for guns to make their way to the streets to be used in crimes.

Asked if more stringent laws would have made it less likely that Brinsley would have gotten hold of a gun, Pierce said, “Maybe if he was living in New York, he might not have been able to get a gun as easily. But there will be arguments on both sides as to whether increasing the restrictive character of laws is going to make you more safe or less safe.”