Lying to the Federal Government is a felony under 18 USC Sec. 1001. This is the crime for which what Martha Stewart was actually convicted. It is a very broad law which covers lying to the Executive, Legislative, or Judicial branches. For a purely hypothetical and far fetched example, if a high ranking Presidential appointee in the Department of Justice knowingly and willfully:
(1) falsifies, conceals, or covers up by any trick, scheme, or device a material fact;
(2) makes any materially false, fictitious, or fraudulent statement or representation; or
(3) makes or uses any false writing or document knowing the same to contain any materially false, fictitious, or fraudulent statement or entry;
to a congressional committee, then that person would be buying a ticket to the hoosegow. Anyone connected to such statements or omissions might be well advised to plead their 5th Amendment rights. If Martha had done so, she may have never tasted jailhouse cafeteria food.
Of course, this is all hypothetical since we all know that no top ranking government officials would lie. You see, this law does not require the person to be under oath when they make the statement or fail to say something. The only elements are: 1) a statement is made or information is omitted that is 2) false or fraudulent and 3) material (basically meaning it matters – lying about shoe size on a HUD statement is not material but it would be if it is a murder investigation where shoe prints are left behind) where 4) the person acted knowingly and willfully 5) within the jurisdiction of the US Government. So, wrangling over whether persons give statements under oath or not seems a bit ridiculous.
Now, for a more practical primer on this particular law since most of us will never get a chance to testify to a congressional committee, this law is why you need to fill out any form that in any way makes its way to the government accurately. This law covers everything from tax returns to HUD statements when buying a home.