CT pistol permit after AR probation?

I has a question regarding my eligibility for a CT pistol permit. About three years ago, I was arrested for 3rd degree larceny and given AR, which I completed successfully. Through a series of childish decisions, I was arrested again for larceny of an item valued at over $1000 (though I'm not sure if it was grand larceny as the item was older and had depreciated in value), but I was given a medical AR due to my OCD. This final two year AR is over in January, and I'm currently in school for nursing with my CNA. My question is this: will either of these arrests or AR's, once dismissed, effect my eligibility to recieve my permit? If so, what could I do about any issues which might arise to ensure that everything would work out ok.