The short answer is that there is no minimum threshold amount. While tax perjury requires that the defendant (taxpayer) knowingly make a false statement that was “material,” this does not require that the statement concern a “substantive” amount. In other words, the standard for “materiality” is not the same as the standard of being “substantive.” As one recent case noted, “The materiality relates to whether there is a misstatement on the return, it does not require the evasion of a substantial tax.” United States v. Kasper, 2011 WL 7098042 (W.D.N.Y. 2011). https://www.leagle.com/decision/In%20FDCO%2020120702C21
If the standard for materiality is not “being substantive”, what is it? The courts have applied two tests to determine what is “material” for purposes of the tax perjury statute, IRC §7206(1).
Under the first, a statement is material if the taxpayer makes a false statement about anything he is required to disclose on the return. This test leads to problems, however. For example, suppose husband and wife file their tax returns separately. They report interest from an asset that is the separate property of the husband on his return, and he pays his taxes. Suppose it turns out that the asset in question is actually a community property asset, and half of the income was supposed to be reported by husband and half by wife. Even though they paid all of their tax liability, they reported the character of the asset incorrectly. If the first test of materiality is used, then technically the couple made a materially false statement, even if they paid all their tax—for they were required to report the proper ownership (and character) of the income.
The other test asks whether “the false statement has a natural tendency to influence, or [is] capable of influencing, the decision of the tribunal in making a determination required to be made.” United States v. DiVarco, 343 F. Supp. 101, 103 (N.D. Ill. 1972). https://leagle.com/decision/1972444343FSupp101_1420.xml/UNITED%20STATES%20v.%20DiVARCO In other words, the taxing authorities ask whether the matter “would have a tendency to influence the IRS in its normal processing of tax returns.” Id.
In DiVarco, the court ruled that a misstatement of the source of one’s income alone, without a misstatement of the amount of one’s income, is a material matter for purposes of the tax perjury statute. The court’s underlying rationale was that if things were otherwise (if the matter were not material) then it would make tax evasion much easier. “To allow taxpayers to wilfully misstate and fabricate the source of their income would thereby render virtually impossible the task of ascertaining whether the amount of income as reported is accurate.” Id.