If the police ask you to take a blood test after a DUI stop, you can refuse. However, if they have a warrant, you cannot legally refuse the test. Therefore, getting such a warrant is the easiest way for the police to determine if you're drunk, if you do not voluntarily submit to the test.
In the past, this created a bit of a problem for the police, and it sometimes still does. Officers used to have to go to the judge's office or even the judge's home to get the paper warrant. Every hour, the person they wanted to run the test on would be about 0.01 percent lower in terms of blood alcohol concentration. If it took hours to get the warrant, the police may come back to find that the driver was now below the 0.08 BAC threshold, even if they felt sure he or she was drunk before.
Today, some officers have the ability to work with on-call judges through smartphones and other such mobile devices. Everything can be done remotely. The electronic warrant can be sent directly from the judge to the officer without the need for travel time, printing or anything else. This can cut back on delays and make sure that the test is done promptly.
Remember that you do have the right to refuse a blood test, and then the police have to get a warrant. If one is conducted without a warrant, that could be a crucial part of your defense, as you could claim that the evidence was illegally obtained and can't be used in court.
Source: FIndLaw, "No-Refusal DUI Enforcement," accessed July 21, 2016