Knowingly and willfully filing an income tax return that the taxpayer knows to be false in some material way is a federal crime.  26 U.S.C. § 7207 provides:

Any person who willfully delivers or discloses to the Secretary any list, return, account, statement, or other document, known by him to be fraudulent or to be false as to any material matter, shall be fined not more than $10,000 ($50,000 in the case of a corporation), or imprisoned not more than 1 year, or both. Any person required pursuant to section 6047 (b), section 6104(d), or subsection (i) or (j) of section 527 to furnish any information to the Secretary or any other person who willfully furnishes to the Secretary or such other person any information known by him to be fraudulent or to be false as to any material matter shall be fined not more than $10,000 ($50,000 in the case of a corporation), or imprisoned not more than 1 year, or both.
 
In cases where the taxpayer filed a false tax return, the Government does not need to prove that it has lost any tax revenue because a false return was filed; even if it is shown that additional taxes are not actually due, the taxpayer can still face penalties because he or she willfully filed a false return.