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The specific law says:
2C:28-4. False reports to law enforcement authorities a. Falsely incriminating another. A person who knowingly gives or causes to be given false information to any law enforcement officer with purpose to implicate another commits a crime of the fourth degree. b. Fictitious reports. A person commits a disorderly persons offense if he: (1) Reports or causes to be reported to law enforcement authorities an offense or other incident within their concern knowing that it did not occur; or (2) Pretends to furnish or causes to be furnished such authorities with information relating to an offense or incident when he knows he has no information relating to such offense or incident.
In any event, saying that you don't know anything about something when you do would not fall under any of these.
While it's roughly a formulation of the law (in that it would cover most witness statements) it is not complete, because it does not cover your situation.
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