There is a penalty for lying on the census.
If you refuse to give out the information or you deliberately give inaccurate information, you can be in legal trouble. According to United States Code, Title 13 (Census), Chapter 7 (Offenses and Penalties), SubChapter II, if you’re over 18 and refuse to answer all or part of the Census, you can be fined up to $100. If you give false answers, you’re subject to a fine of up to $500. If you offer suggestions or information with the “intent to cause inaccurate enumeration of population,” you are subject to a fine of up to $1,000, up to a year in prison, or both. Here’s the official verbiage:
221. Refusal or neglect to answer questions; false answers
(a) Whoever, being over eighteen years of age, refuses or willfully neglects, when requested by the Secretary, or by any other authorized officer or employee of the Department of Commerce or bureau or agency thereof acting under the instructions of the Secretary or authorized officer, to answer, to the best of his knowledge, any of the questions on any schedule submitted to him in connection with any census or survey provided for by subchapters I, II, IV, and V of chapter 5 of this title, applying to himself or to the family to which he belongs or is related, or to the farm or farms of which he or his family is the occupant, shall be fined not more than $100.
(b) Whoever, when answering questions described in subsection (a) of this section, and under the conditions or circumstances described in such subsection, willfully gives any answer that is false, shall be fined not more than $500.
(c) Notwithstanding any other provision of this title, no person shall be compelled to disclose information relative to his religious beliefs or to membership in a religious body. Sec. 222. Giving suggestions or information with intent to cause inaccurate enumeration of population Whoever, either directly or indirectly, offers or renders to any officer or employee of the Department of Commerce or bureau or agency thereof engaged in making an enumeration of population under subchapter II, IV, or V of chapter 5 of this title, any suggestion, advice, information or assistance of any kind, with the intent or purpose of causing an inaccurate enumeration of population to be made, shall be fined not more than $1,000 or imprisoned not more than one year, or both.
“SubChapter II, if you’re over 18 and refuse to answer all or part of the Census, you can be fined up to $100.”
And THAT is not enforced.
I, personally, would not answer whether or not I had served in the military, and nothing has come of it.