That's certainly true in a broad and general sense, on the federal level, although most states have adopted a good deal of the common law.
But Alexander Hamilton and the Supreme Court have both told us that the Constitution was written in the language of the legal system that was in place at the time, and the terms in it were derived from our English heritage and the English common law.
And Vice Chancellor Sandford in Lynch v. Clarke (1844) would disagree with that statement in regard to natural born citizenship.
“The term citizen, was used in the constitution as a word, the meaning of which was already established and well understood. And the constitution itself contains a direct recognition of the subsisting common law principle, in the section which defines the qualification of the President… The only standard which then existed, of a natural born citizen, was the rule of the common law, and no different standard has been adopted since. Suppose a person should be elected President who was native born, but of alien parents, could there be any reasonable doubt that he was eligible under the constitution? I think not. ”
The United States Supreme Court approvingly quoted Sandford's decision in US v. Wong Kim Ark (1898), and they said essentially the same thing: That the same rule had always applied, first in England, then in the Colonies, then in the United States after Independence, then in the United States after the establishment of the Constitution.
Lynch v Clarke - New York state.
State law. You just can’t help yourself can you?
Of all the doctrines which have ever been broached by the federal government, the novel one, of the common law being in force and cognizable as an existing law in their courts, is to me the most formidable. All their other assumptions of un-given powers have been in the detail. The bank law, the treaty doctrine, the sedition act, alien act, the undertaking to change the State laws of evidence in the State courts by certain parts of the stamp act, &c. &c. have been solitary, unconsequential, timid things, in comparison with the audacious, barefaced and sweeping pretension to a system of law for the United States, without the adoption of their legislature, and so infinitively beyond their power to adopt.
Madison letter to Jefferson, Jan 18, 1800
Madison states that admitting the common law as legal federal law of the United States "would confer on the judicial department a discretion little short of a legislative power" since federal courts would "decide what parts of the common law would, and what would not, be properly applicable to the circumstances of the United States" and thus would "erect them [judges] into legislators"