Not sure if you have to pay for the blood test (it wouldn’t surprise me), but part of driving on a public road is consenting to a breathalyzer test. They do need a warrant to draw your blood against your will, but they may bully the hospital into doing it anyway. Refusing to take one is a crime that in combination with any other violation can get your license suspended.

It may be worth going that route if you are marginally over the limit and a few hours would sober you up.