Connecticut has 169 municipalities, 168 of which have their own zoning regulations. Many of them also have at least a few firearms ordinances, which may or may not be (but probably are) more restrictive than state law.
Indeed. And any municipality that's rural enough to allow the discharge of firearms at all probably has someone at the town hall who knows the zoning regulations and is willing to answer questions. When in doubt, ask -- it's a good way to stay legal.
And with that, I'm going to close this. The OP's question has been answered, and other states' laws aren't relevant to that question.