New York Consolidated Laws, Criminal Procedure Law - CPL § 60.20 Rules of evidence;  testimonial capacity;  evidence given by children

1. Any person may be a witness in a criminal proceeding unless the court finds that, by reason of infancy or mental disease or defect, he does not possess sufficient intelligence or capacity to justify the reception of his evidence.

2. Every witness more than nine years old may testify only under oath unless the court is satisfied that such witness cannot, as a result of mental disease or defect, understand the nature of an oath.  A witness less than nine years old may not testify under oath unless the court is satisfied that he or she understands the nature of an oath.  If under either of the above provisions, a witness is deemed to be ineligible to testify under oath, the witness may nevertheless be permitted to give unsworn evidence if the court is satisfied that the witness possesses sufficient intelligence and capacity to justify the reception thereof.  A witness understands the nature of an oath if he or she appreciates the difference between truth and falsehood, the necessity for telling the truth, and the fact that a witness who testifies falsely may be punished.

3. A defendant may not be convicted of an offense solely upon unsworn evidence given pursuant to subdivision two.