If you completed the terms of your AR and the carges were "dismissed" and not "Nolle'd" meaning no lo contendre (a latin term meaning that you agree the state had the pc to arrest you, however the state is reserving the right of prosecution to see if you stay out of trouble for the next 13 months, in which case the charges are dismissed) which would extend your probation another 13 months. If the probation period is over, and the charges are indeed dismissed,and there was not "nolle" time pending, then you should have no hassle getting your permit. Whatever you do, dont lie about geting arrested and the charges against you. False statements on the application will get you denied for eternity, and arrested for false statement.
Depending on the charges you may be denied by your town. If your arrest was for certain charges then 2 years isnt that long ago to deny you a permit, regardless of the outcome in court.
Keep in mind also, people get deals every single day in this state. NOBODY goes to for a first arrest unless they kill more than 2 nuns. Not in CT.
And you get AR once. Its a one shot deal, use it once and its gone forever.