A number of states, like Arizona, allow the police to do a blood draw in some DUI cases without a warrant. In other words, the cops don't even have to ask a judge. They can just take you to the hospital or mobile lab and get your blood drawn, probably while you're still in handcuffs.
But this might come to an end (or happen less often) because the U.S. Supreme Court has ruled that law enforcement needs a warrant before taking your blood. Bill Mears with CNN reports that the Court found in favor of people accused of DUI. The cops must first get a warrant; otherwise, it would be an unreasonable search and seizure.
Mears quotes Justice Sonia Sotomayor's opinion in that DUI investigations don't always require the immediate testing of blood without a warrant.
In other words, the cops can't say they needed to draw blood first for fear that a DUI suspect's blood alcohol content would decrease in the time it would take to get a warrant. But the warrantless blood draw will likely continue, which would occur in felony DUI cases, where someone was injured or killed.
Source: Supreme Court rules against police in drunk driving case