Open space does not mean the whole town. Open space is land which the town wants to preserve/protect for one reason or another. This is from the DEP website;
Connecticut’s natural diversity and scenic beauty add immeasurably to the quality of life of its residents. The state’s prosperity has always depended upon its natural resources. Forests and farms contribute to a healthy and diverse economy. Parks and open lands improve the quality of life and help attract businesses. Natural areas and waterways provide critical wildlife habitat, clean drinking water, and scenic natural beauty, which is the foundation of the tourism industry. However, not all undeveloped land is protected open space; some of it will eventually be developed. For Connecticut to remain an attractive state in which to live, work and conduct business, it is critical that development be balanced with land conservation. 1) valuable for recreation, forestry, fishing, conservation of wildlife or natural resources; 2) a prime natural feature of the state's landscape; 3) habitat for native plant or animal species listed as threatened, endangered or of special concern; 4) a relatively undisturbed outstanding example of an uncommon native ecological community; 5) important for enhancing and conserving water quality; 6) valuable for preserving local agricultural heritage; or 7) eligible to be classified as Class I or Class II watershed land.
As far as the Naugatuck ordinance, usually a borough is a subsection of a town but it seems in this case it is the whole town. The penalty for that violation seems to be a $100 fine;
Sec. 1-7. - General penalty; continuing violations.
Whenever in this Code or in any ordinance or resolution of the borough any act is prohibited or is made or declared to be unlawful or an offense, or whenever in such Code, ordinance or resolution the doing of any act is required or the failure to do any act is declared to be unlawful, where no specific fine or penalty is provided therefor, the violation of any provision of this Code or any such ordinance or resolution shall be punished by a fine not exceeding one hundred dollars ($100.00); each day any violation of any provision of this Code or of any such ordinance or resolution shall continue shall constitute a separate offense.
In addition to the fine or penalty hereinabove provided, any condition caused or permitted to exist in violation of any of the provisions of this Code or any such ordinance or resolution shall be deemed a public nuisance and may be, by the borough abated as provided by law, and each day that such condition continues shall be regarded as a new and separate offense.
In all cases where the same offense may be made punishable, or shall be created by different clauses or sections of the ordinances of the borough, the prosecuting officer may elect under which to proceed; but not more than one (1) recovery shall be had against the same person for the same offense.
Obedience to the provisions hereinafter set forth may be enforced by criminal information for the penalties herein prescribed as well as by prosecution of the offender as provided in this section or by civil action for a penalty, or by civil remedy at law or equity by way of injunction, or otherwise to abate or prevent a violation of the provisions of this Code of Ordinances. Neither a judgment in, nor the pendency of a criminal prosecution for an alleged violation of the provisions of this Code, nor a judgment in or the pendency of a civil action at law or in equity shall be a bar to the other form of proceeding. The imposition of a penalty for a violation of this Code shall not excuse the violation or permit it to continue, and the remedies herein provided for penalties and civil action to enjoin or abate a violation shall be cumulative.
I would say this is another outdated municipal ordinance that is not used and most likely forgotten. I would bet that most if not all of the LEO's would not even know it exists and even then it's a $100 fine. As a LEO here in CT I would say that you would be fine with the pistol permit. If not, call the PD or the town or both to make sure. If you were in my town, I would be go by state law.