Sen. Richard Blumenthal (D-Conn.) introduced legislation on Tuesday that would require background checks for buying gun ammunition.

It’s currently illegal to sell ammunition to fugitives, felons and people suffering from mental disorders. However, while background checks are required for selling firearms, they are not required for selling ammunition. Blumenthal’s legislation would require background checks for selling ammunition as well.

“Ammunition sales should be subject to the same legal requirements as firearm sales — instant background checks using the FBI’s national database,” Blumenthal said in a statement. “There is no rational reason why a person can walk into a store, fill their shopping cart with hundreds of rounds of ammo, pay up, and walk out without so much as giving their name.