Can you get in trouble for "misidentifying" race?

I have seen recent posts on social media of people posting people, usually convicts of afro-hispanic, black, or south asian descent being labeled as "racially white' on police reports in America. These are not "well he's a puerto rican guy who looks mixed and he marks white", as in these people would be expected to put asian or black as their racial category.

A while back someone told me they heard white people who marked black for some form, I believe it was for benefits of something, got in hot water legally for it, but they didn't show me any proof.

Most people in the west also know the story of Elizabeth Warren, who is somewhere around 1% indigenous/native american, the rest being northwestern european, putting "indigenous" alone with no "indigenous and white" when applying as a professor, which is the equivalent of a hungarian person putting their race down as asian.

If you guys have any links of news stories or anything I'd like to see.