When we left the Questura in Vasto, they just said we would receive an SMS when they were ready. But we got to thinking about all the comments about checking on line, and did some searching. We found this site. Polizia di Stato
At the site they instruct you to put either the File Number, or Registered Mail Code for your application. We never did figure out where a file number might be located, but we did have a receipt from the Post Office when we turned our application in.
At the top there were two numbers. One labeled Password and the other User ID. No additional clues on the receipt about where one might use these items. BUT!! I tried the Password in the Poliza input field and bingo, it told me my Permesso was in process.