I have not found a case directly on point, but there is a case in the right neighborhood.
In Flordia v. Carter 364 So. 2d 1249, Carter was charged with perjury for making a false statement under oath. He recanted his testimony in a letter to the defense attorney the next day. Subsequently he was charged with perjury: the trial judge dismissed the case based on his having recanted (which is a defense to perjury). The judge said (quoted in the appeal below and citing a relevant precedent Brannen v. Florida 114 So. 429)
It matters not whether Carter knew his original testimony was false or
whether he was merely mistaken. "The law encourages the correction of
erroneous and even intentionally false statements on the part of a
witness, and perjury will not be predicated upon such statements when
the witness, before the submission of the case, fully corrects his
The lower appeals court rejected the trial court's dismissal, saying
Recantation is a defense to an allegation of perjury only where there
is an acknowledgement of the falsity of the original sworn statement,
a voluntary retraction of that statement, and a new statement which
discloses the true facts. It is not a viable defense where the
perjured testimony has substantially affected the proceeding or it has
become manifest that such falsity has been or will be exposed.
Otherwise, one could rest on his lie, allowing it to substantially
affect a proceeding, and never retract unless the falsity had been
exposed. This would provide no inducement or encouragement to tell the
That court basically felt it was based on the threat of being discovered, and felt that a particular state statute had taken away the recantation defense, so they reinstated the charge.
The appeal to the Florida Supreme Court, Carter v. Florida 384 So. 2d 1255 basically declared that the appeals court was wrong about the statute (they officially held that recantation is a defense to perjury). They concluded that Carter gained nothing by recanting (that was a distinguishing feature in a precedent that the lower court favored).
The dissent in this decision opined that
It may be that the false deposition testimony by Dr. Carter was
inadvertent and without criminal intent.... These, however, are
factual issues and should be resolved by a jury rather than by the
trial court on a motion to dismiss.
What unifies all opinions on the matter is that a false statement made under oath must be recanted. The reason why Carter was not convicted was that he (possibly) was unaware that his testimony was false and he did recant when he became aware of the facts.