The instructions for obtaining your permit are on the form: http://www.ct.gov/despp/lib/despp/sl.../dps-799-c.pdf
Anything other than what is listed here is probably not lawful. http://ctcarry.com/PermitRequirements/Requirements
There is no 'question' about getting the form authorized. It is clear that the application must be notarized on the application.
You can get fingerprinted anytime. If Danbury gives you an issue, just go get it done elsewhere.
Danbury has to accept your permit at any time. If they don't accept it in person, just mail it via certified mail.
If you have additional questions/issues: permitissues [at] ctcarry.com