Most of the time, no. There are some exceptions to this rule. In Ohio, an officer can use "whatever reasonable means necessary" to take a blood sample if the suspect has two or more OVI convictions within the previous six years. If the suspect is unconscious, he or she has consented to the blood test. There is also a US Supreme Court case, Schmerber v. California, that allows officers to forcibly take blood without a warrant. However, facts must support that additional delay would cause the evidence to dissipate. The high court specifically warned against more expansive interpretations of its decision beyond the facts of the case at hand. Ohio officers would have a hard time using the Schmerber exception because the State gives the officer three hours to obtain the blood sample. It is also important to note that Schmerber was decided in 1966. We have experienced numerous improvements in technology and transportation over the previous 66 years that make it easier to obtain a signed search warrant.
However, last month the high court has decided to revisit the issue. A Missouri trial court ruled that a warrantless blood sample violated the defendant's Constitutional right to be free from unreasonable search and seizure under the Fourth Amendment. On appeal, the Missouri Supreme Court held that an officer must obtain a search warrant before taking blood without the suspects consent.
This decision will likely come out early next year and will have obvious implications in Ohio. On one side, a police officer may be able to cart anyone suspected of OVI to a medical facility to obtain a blood sample. On the other, part of Ohio's OVI statute could be found Unconstitutional.