All states disqualify you from receiving unemployment benefits if you make a false statement to Unemployment personnel. You cannot intend to mislead unemployment personnel or know that your statements would cause Unemployment personnel to be misled. If you accidentally give false information, that is not a basis for disqualifying you from receiving your unemployment benefits.
Some states disqualify you from receiving unemployment benefits for failure to disclose information or concealment. If you know that the information that Unemployment Personnel is looking for and knowingly keep that information from them, you will not receive unemployment benefits.
Most of the time when you are charged with making false statements, the Unemployment Personnel will not leave it a just a disqualification and you can be prosecuted for those lies and intentional disclosures. If you are convicted, you can be fined or even sent to jail for the offense.