See the section on "what to expect if you don't comply": https://www.ftc.gov/enforcement/competition-matters/2019/03/ftc-takes-its-subpoenas-cids-seriously-you-

See the section on "what to expect if you don't comply": https://www.ftc.gov/enforcement/competition-matters/2019/03/ftc-takes-its-subpoenas-cids-seriously-you-should-too https://www.ftc.gov/enforcement/competition-matters/2019/03/... The relevant statute looks to be 15 U.S.C. § 57b–1(e); if you don't comply with the request they seek judicial enforcement, so they just ask a judge for a court order, at which point failure to comply is definitely illegal.