The Minnesota Court of Appeals has just held that a criminal charge of refusal to submit to a warrantless search of their blood is unconstitutional! In State v. Trahan, the Minnesota Court of Appeals held that a fundamental right is implicated when a person refuses to give the state their blood, and therefore, at least without a warrant, this charge is not constitutional.
As of now, it seems clear that the State can prevail on charges of refusal to submit to a warrantless breath test. Minnesota appellate courts have not had a decision in this capacity with respect to urine (blood, breath, and urine are the three types of alcohol tests used in Minnesota).
It is likely that this particular case will be appealed to the Minnesota Supreme Court, which may bring more clarity to this issue. Until then, this is a published, binding decision that may affect many cases throughout Minnesota.