I moved out of state. Called the NFA customer service number (304) 616-4500. They had me write a letter with the serial numbers. They sent a fallow up letter To keep with my form 4's. I would call just to be safe. Better 10 minutes out of your day then a ATF visit by a Agent having a bad day.
Hope that helps.
While RangerWalker is correct that it is better safe than sorry (and keep a note of who you talk to and the date/time, what was said), technically speaking you are only required to notify/fill out paperwork when you move out of state.