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New York City Mayor Michael R. Bloomberg, co-chairman of Mayors Against Illegal Guns, also argues that some specific changes can lower crime rates. He told the U.S. Conference of Mayors last week that after Colorado closed its loophole allowing private dealers to sell guns without conducting background checks, fewer Colorado-sold guns turned up at crime scenes.

He also said that in states that require background checks on all sales, 38 percent less women are fatally shot by their boyfriends and husbands.

He also cited a recent Duke University study that showed once a severely mentally ill person’s records are turned over to the background check system, that person is 31 percent less likely to be convicted of a violent crime.

• Luke Rosiak contributed to this report.