As for the immigration question you need to speak with an expert in that area of the law. There are many here on Avvo. If your case was dismissed and you have the paperwork from the court you don't need anytyhing else.
This is not intended to create an attorney-client relationship. It is absolutely NOT legal advice that you should rely upon when making a decision. It is general information about the law in Connecticut. You need to consult with an attorney who will ask you all the facts necessary to give you specific legal advice for your situation.
I agree with atty Black. You should get, however, a certified copy of the disposition showing the dismissal; get it from the clerk at the court.
You'll need that for immigration.
Attorney Bonanno's answers to questions are for general purposes only and do not establish an attorney-client relationship. You should carefully consider advice from an attorney hired and who has all facts necessary to properly advise a client, which is why these answers to questions are for general purposes only and do not establish an attorney-client relationship.