States such as Arkansas do not require a background check for guns if you have a concealed carry permit.
Although a gun dealer will almost always run a background check.
All states require background checks of you're purchasing from a licensed firearm dealer, as that's federal law.
Some (most) states that issue concealed carry permits will waive to background check if the buyer presents a valid permit from that state.
However Arkansas itself as a state does not Arkansas has no state law requiring firearms dealers to initiate background checks prior to transferring a firearm.
When someone tries to buy a firearm, the seller—known as a Federal Firearms Licensee (FFL)—contacts the FBI.
The prospective buyer fills out the required form, and the FFL sends that information to the FBI.
The FBI itself then performs a background check on the buyer to verify eligibility.
Current federal law requires background checks to be performed for anyone purchasing a firearm at a federally licensed gun dealer–however only 40% of guns sold in the US are sold through a federally licensed dealer.
In most states, sales at gun shows, flea markets, and private gun sales are not subject to regulations.
Federal law does not limit the number of guns a person may buy in any given time period.
However, federal law does require federal firearm licensees (“FFLs”) to report multiple sales of handguns to ATF and other specified law enforcement agencies.
If someone is hospitalized on a “5150 Hold” (Welfare & Institutions Code § 5150) in California after police take that person into custody because it is determined the individual is a danger to herself or himself or others, he or she may not possess a firearm or any other deadly weapon for five years after being released.