It is a federal crime to make a material false statement in a matter within the jurisdiction of a federal agency or department. This is an overview of federal law relating to the principal false statement and to the three primary perjury statutes. In outline form, Section 1001(a) states the following: 
I . Section 1001(b) creates an exception, a safe harbor, for statements, omissions, or documentation presented to the court by a party in judicial proceedings. One proscribes false statements in matters of legislative branch administration and reaches false statements made in financial disclosure statements. The other proscribes false statements in the course of congressional investigations and reviews, but does not reach false statements made concurrent to such investigations or reviews. § 1621(1), a defendant's false statement must be material." § 1621(2))

Congress added Section 1621(2) to the general perjury statute in 1976 in order to dispense with the necessity of an oath for various certifications and declarations. Perjury in a Judicial Context (18 U.S.C. § 1623)

Congress enacted Section 1623 to avoid some of the common law technicalities embodied in the more comprehensive perjury provisions found in Section 1621 and thus "to facilitate perjury prosecutions and thereby enhance the reliability of testimony before federal courts and grand juries." statement, under penalty of perjury as permitted under [Section] 1746 of title 28, United States Code; I II . Conviction does require a showing, however, that the two statements were made under oath; it is not enough to show that one was made under oath and the other was made in the form of an affidavit signed under penalty of perjury. § 1622)

Section 1622 outlaws procuring or inducing another to commit perjury: "Whoever procures another to commit any perjury is guilty of subornation of perjury, and shall be fined under this title or imprisoned for not more than five years, or both." Conspiracy under Section 371 is punishable by imprisonment for not more than five years. When the defendant is convicted of a crime other than perjury or false statements, however, perjury or false statements during the investigation, prosecution, or sentencing of the defendant for the underlying offense will often be treated as the basis for enhancing his sentence by operation of the obstruction of justice guideline of the U.S.
Federal courts, Congress, and federal agencies rely upon truthful information in order to make informed decisions. Federal law therefore proscribes providing the federal courts, Congress, or federal agencies with false information. The prohibition takes four forms: false statements; perjury in judicial proceedings; perjury in other contexts; and subornation of perjury.
Section 1001 of Title 18 of the United States Code, the general false statement statute, outlaws material false statements in matters within the jurisdiction of a federal agency or department. It reaches false statements in federal court and grand jury sessions as well as congressional hearings and administrative matters but not the statements of advocates or parties in court proceedings. Under Section 1001, a statement is a crime if it is false regardless of whether it is made under oath.
In contrast, an oath is the hallmark of the three perjury statutes in Title 18. The oldest, Section 1621, condemns presenting material false statements under oath in federal official proceedings. Section 1623 of the same title prohibits presenting material false statements under oath in federal court proceedings, although it lacks some of Section 1621's traditional procedural features, such as a two-witness requirement. Subornation of perjury, barred in Section 1622, consists of inducing another to commit perjury. All four sections carry a penalty of imprisonment for not more than five years, although Section 1001 is punishable by imprisonment for not more than eight years when the offense involves terrorism or one of the various federal sex offenses. The same five-year maximum penalty attends the separate crime of conspiracy to commit any of the four substantive offenses.
A defendant's false statements in the course of a federal criminal investigation or prosecution may also result in an enhanced sentence under the U.S. Sentencing Guidelines for the offense that was the subject of the investigation or prosecution.
This report is available in an unabridged form—with footnotes, quotations, and citations to authority—as CRS Report 98-808, False Statements and Perjury: An Overview of Federal Criminal Law.