It is hard to tell in the current gun control frenzy in this state. Immediately upon passing the newest gun control bill, a purchaser of rifles or shotguns must pass a national criminal background check. While your charges were nolled, there still is a record of the charges. This new law may prevent you from purchasing based on the background check alone, but that remains to be seen.
Being domestic offense charges, even though nolled, the charges will probably prevent you from obtaining a pistol permit. The state police have a wide discretion when it comes to approving a permit application. In CT, a pistol permit is a privilege, not a right. Therefore it can be denied for the smallest of reasons. You do have the right to appeal the decision, but that is extremely rarely successful.
Brian S. Karpe, Esq. (860) 242-2221 Note: This response DOES NOT constitute legal advice and therefore no specific action should be taken in reliance thereon. No attorney-client relationship is created through this response. You should speak to an licensed attorney in your state who is competent to answer your question before taking any action with regard to this question.