SCOTUS ruled very strictly on this in 1998. James Brogan was visited by Federal agents at his home and asked if he had accepted illegal cash payments from a company. Brogan simply answered "No."
SCOTUS upheld his conviction for this under U.S.C. § 1001. His only legal options were to say “Yes” or state his choice to exercise his 5th amendment right to remain silent.
Similar laws apply to interactions with pretty much any LEO in any US state, though the lie must be material to a criminal investigation. Note that some states make nearly everything a misdemeanor crime (like speeding 5mph over the limit) whereas other states make many of those things civil infractions.
Isn't lying to a federal investigator also a crime? Searching suggests 18 U.S.C. § 1001.