The United States Supreme Court held in Missouri v. McNeely that forcing an unwilling suspect to have their blood drawn without first securing a warrant is a violation of their Fourth Amendment rights. The Supreme Court concluded that the exigency exception to the warrant requirement did not apply in routine DUI cases because the simple fact that blood alcohol levels dissipate over time did not constitute an emergency.
In drunk-driving investigations, officers must typically take the suspect to a medical facility so that a trained medical professional can conduct the blood draw. There is an automatic delay between when the arrest occurs and when the blood is taken, regardless of if there is a warrant, causing a suspect's BAC to dissipate.
If a police officer can reasonably obtain a warrant during this time, the Fourth Amendment mandates they do so. Therefore, a warrant is necessary before obtaining a blood sample in "routine" DUI cases; however, if other factors are present (i.e. an accident) the courts will look to the totality of the circumstances in determining whether exigency exists in those situations.