It depends on where you buy the gun. Different states do different things.
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In Arizona they don't register the gun to who bought it. Well, they didn't when I bought my pistol there, about 15 year ago or so. I was stopped in California after I had moved there. With out going into detail about why they knew I had a pistol in the car with me, they found it. When they ran the serial number, nothing about ownership came up, just that it was sold. There were two officers when this happened. One wonders why there was no information about me buying it. When I explained that I bought it in Arizona when I lived there, the other officer knew and explained to the the other that Arizona didn't register purchases to an individual. Since I hadn't done anything illegal, and the gun and me were legal, They gave me my pistol back and let me go.
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Other states register gun purchases to the individual that buys it, and that's all that comes up. In some states, when a person sells a gun privately, you have to notify the state that there was a private sale made, and the gun is register to the new buyer. Other states do not require notification or a private sale. In that case, a gun could be transferred, legally, multiple times. And when police run that serial number, it will come back to the original purchaser. If the gun was used illegally, they will contact the original purchaser, and go from there. Trying to follow the purchases/transfers, if they can. People don't always keep track of who they sell a gun to. It's a good idea, to cover your ass in case the gun is used illegally. And if you knowingly sell the gun to some one that isn't allowed to own guns, then you're in a world of shit. So if you're selling a gun, be careful and get any information one the buyer that you can, and keep it.
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Mar 10, 2014 - Before you purchase a firearm through a private sale I would recommend that you utilized the below link to ensure the firearm is not stolen.