Go to this site www.ctgunrights.com and scroll to the bottom of the main page. Click on the link "Suggestions to speed up the Permit to Carry application process". This document has lots of great information. However, at this point what you should do is ask them if and when they received the "STATE AND FEDERAL CRIMINAL HISTORY RECORD CHECKS FROM THE COMMISSIONER OF PUBLIC SAFETY". By law they have one week from the date of receipt of that information to make a decision.
If you ask them specifically about the status of your permit, you will get the run-around as you have already found out.
Best of luck.