Hough was at the Casamigos Tequila party in Hollwood ... and dressed up as Crazy Eyes -- the popular character from "Orange is the New Black."
We're pretty sure Paula Deen would have been skewered if she did it. So we gotta ask ...
12:10 PT -- Julianne took to Twitter to apologize for offending anyone with the costume explaining, "It certainly was never my intention to be disrespectful or demeaning to anyone in any way."
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