I know they have the rules in my state correct in their chart below. http://www.guardian.co.uk/world/interactive/2013/jan/15/gun-laws-united-states
We don't know if she had one or not. NBC News reported they were legal guns. According to the CNN News segment, Time Magazine said they couldn't find a permit under Nancy Lanza’s name. You would think that Time Magazine could ask the police about the permit, but it sounds like the records are sealed on this case. So maybe that is why Time Magazine tried to do their own search.
maybe under her ex’s name?