I don't know how as all the states do a criminal background check which requires a social security number. The difference between the states is how long the check takes. Here in Missouri they do it over the phone. From the time I pick out the gun to out the door is all of 10 minutes.
All states are now on the NICS system, which is run by the feds. That's what they use your soc. sec. # for. Sure sucks to have a common name for that stuff.