No, but as explained below, you might be in violation of other statutes. For the government to find that a person committed tax perjury, it must show, among other things, that the document with a false statement was made under the penalty of perjury. Thus, if the document submitted to the IRS (or other taxing authority) was not made under penalty of perjury—i.e. there was no sworn declaration—then one cannot be found guilty of tax perjury.
The usual income tax return, Form 1040, contains the required declaration that its contents are submitted under penalty of perjury:
“Under penalties of perjury, I declare that I have examined this return and accompanying schedules and statements, and to the best of my knowledge and belief, they are true, correct, and complete. Declaration of preparer (other than taxpayer) is based on all information of which preparer has any knowledge.”
Some taxpayers have tried to outsmart the IRS regarding the above declaration by crossing that language off when they submit their tax return. If the taxpayer files as just described, he or she can effectively avoid possible prosecution under IRC §7601—but the government could then assert a violation of the failure to file a tax return under IRC § 7203. https://www.law.cornell.edu/uscode/text/26/7203
Moreover, the taxpayer might be guilty of violating other statutes. For example, submitting a false document to the government is a crime under 18 U.S.C. § 1001. That statute provides that a person commits a crime, punishable by up to 5 years (and 8 years in certain other cases), when he or she “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 it contains a materially false, fictitious, or fraudulent statement or entry. https://www.law.cornell.edu/uscode/text/18/1001
Similarly, although not tax perjury, a person could be found to have committed a felony under IRC § 7206(2) for submitting a false document to the IRS. That Code Section provides that a person commits a felony whenever he or she “willfully aids or assists in, procures, counsels, or advises regarding the preparation or presentation, or in connection with any matter arising under, the internal revenue laws, of a return, affidavit, claim, or other document, which is fraudulent or is false as to any material matter, whether or not such falsity or fraud is with the knowledge or consent of the person authorized or required to present such return, affidavit, claim, or document.” https://www.law.cornell.edu/uscode/text/26/7206 In other words, if a person helps another prepare a false document to submit to the IRS, it can be a felony, even if it is not tax perjury.