Yes.  If you are being investigated by the Federal Government and lie to a federal law enforcement agent or United States Attorney, you can be prosecuted and charged with a violation of 18 U.S.C. § 1001 for making a false statement.  While it is not a crime to lie to law enforcement conducting a state investigation nonetheless, you could be charged with obstruction, filing a false instrument or perjury if your false statement were written or otherwise provided during sworn testimony. It is recommended that you consult with and/or hire an attorney PRIOR to discussing anything with law enforcement.