You don't. The tax stamp application is the "permit" even though it is just proof the tax was paid. The ATF form 4 is sent in with a check for $200, fingerprints, photos then approved in several months and the buyer takes the MG home. The ATF is required by law to consider each application they receive.
The Obama administration did away with the CLEO signature as the most common complaint from NFA firearm owners back then was refusal by the local sheriff to sign. I always thought refusing to sign was stupid; the buyer or maker would just form a LLC or trust to own the firearm instead. Obama's 41F just requires that that the applicant send a copy of the application to the local sheriff now.
It is entirely routine; the ATF is not that picky either. One time I misspelled my name on an application; they approved it. Another time I forgot to sign the form, it was approved and sent back with a post-it note saying I needed to sign my copy.
No states completely ban machine guns. If I remember correctly all but a dozen states allow unlicensed people to own machine guns, the rest require an FFL/SOT. The FFL/SOT is also a routine matter, but the ATF gets more involved in the approval process.
I'm unlikely to ever own a machine gun due to the expense of the pre-86 guns and the expense of the FFL ($200/3 years) and SOT ($1000/year) for the post-86 dealer samples.
