In my case they were mailed a letter with a form on which they needed to check off the boxes & return to the local PD. The checklist contained the typical questions asked on the app itself... Has this person been convicted of a crime? etc...
G1-Niners Club #0007
Even though I had to give references with each purchase I made in NJ they were only contacted the first time. IIRC, they were called and asked how long they knew me, if I was responsible, level-headed, sane, etc. Both references said the call only took a minute or two. Of course, that was back in about 1995 so it may be done by mail now.
S&W 642, 686 Plus