Most crimes in the U.S. are prosecuted on the state level under state laws. This includes hate crimes and each state has its own version of hate crime legislation. There are also federal hate crime laws, but unless the circumstances are extraordinary, federal officials usually defer to their state counterparts.
Hate crimes themselves are considered “penalty enhancements” in which state and federal prosecutors can charge a person with an additional penalty that adds to the punishment. For example, a misdemeanor assault can be elevated to a felony charge with greater punishment if prosecutors add a hate crime charge.