Swift - what is stated as applicable to the state of Connecticut does not define or redefine the Constitution.
The Tenth Amendment: “The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.”
There is no all encompassing federal election law, except dealing with campaign finance. Each state plus the District of Columbia determines who is eligible under the Constitution to run for office in that state.
If any state passed a law stating that two American citizen parents were required in order to be eligible as a natural born citizen, I’m certain that law would be challenged at the Supreme Court of the United States and we might finally get a definitive clarification. But no state has passed such a law and neither has Congress.
The current interpretation of Article 2, Section 1 is that a person born in the United States is a natural born citizen, as long as they do not hold diplomatic immunity or they are not a member of a foreign invading military.