In general, states handle driving under the influence offenses. But there are situations in which you could face a DUI at the federal level.
If you are driving under the influence or an officer suspects you are under the influence of drugs or alcohol when behind the wheel on federally-owned land, you could face a DUI at the federal level instead of one in state court.
State vs federal
In general, the penalties for any federal crime will be harsher than those at the state level. You will usually have to pay much higher fines and fees associated with a federal charge. Jail or prison time may also be higher. An arrest for a misdemeanor, for example, could carry up to six months in jail, five years of probation and a fine of up to $5,000. In some cases, though, the federal officers will defer to state guidelines for punishment.
Federally owned land includes various areas throughout the country. All courthouses and surrounding property are federal land. National parks, monuments and historic locations are also in this category. Airports and military bases are national land as well. Any place the federal government owns counts as federal land.
Due to the serious nature of this type of charge, it is imperative to know your rights and to understand the exact charges you will face. You may have a difficult time navigating the federal legal system as it is different from the state system. It can also be quite stressful to deal with a charge at the federal level as it may have higher stakes than you would have in state court.