Per CT Law Section 29-28a:
Your PD is breaking the law. Get a lawyer and have them call. Report the local PD to the State and your state representative. Don't let bad LEOs get away with ignoring the law. That part of the statute was written specifically to stop what you are experiencing.
While the locals are in violation of the law when they ignore the 8 week period there is no punishment listed in the statute if they do so.
Its why some towns (usually the larger ones like New Haven and Bridgeport) intentionally ignore the 8 week period and drag their feet when issuing the permit. Back in 08, New Haven took
six months to issue my temporary permit. During the long wait, I called all sorts of people; DPS, SPFU, Board of Firearms Permit Examiners. Everyone said the same thing, its a known issue that some towns intentionally drag their feet and until your denied there isn't much you can do about it short of getting a lawyer and filing a lawsuit.
The Board of Firearms Permit Examiners person I spoke with said that one could file to start the appeals process, but they are backlogged (as much as a year or more).
The Board of Firearms Permit Examiners has issued a statement recently that the local issuing authority can no long ask for items beyond what the state form indicates. That means that you cannot be denied for not providing letters of recommendation, submitting to an interview, not submitting the invasive background check document that NHPD had (that one was a piece of work, everything in your life was reviewable).
It sucks that some towns feel the need to screw with people, but the good news is so long as you eligible for the permit you will eventually get it. And the state permit can be gotten the same day, and once the state permit is in hand you can buy pistols immediately.
One thing for those who haven't gone through the pistol permit process yet. Some recommend going for the Eligibility Certificate first. That is done by the DPS and is done fairly quickly. Then submit that certificate with your pistol permit application and hopefully the process will go much quicker. Both application requirements (and background checks) are similar. The major difference being with the certificate you cannot carry the pistol outside the home.