The issue of whether or not the police offered an independent blood test comes up fairly regularly. Often times, those arrested for DWI/DUI do not remember being offered an independent blood test. Just as frequently, they flat deny that an independent blood test was offered. It then becomes a simple matter of who the court or jury believes, the DWI/DUI defendant or the police officer. This is typically not going to end favorably for the defendant.
If you blow over .08 on the breath alcohol test, then you should request an independent blood test. The officer may not tell you your breath score. If you find yourself in the midst of the booking process, then rest assured you need to request a blood alcohol test.
The breath test have an error rate of at least 10%. There are numerous individual or situational factors that may elevate the score as well. If you have only had a little to drink, it is critical that you get a blood draw since these other factors may be at work. The blood test is far more accurate and may be significantly lower as a result of these factors.
You should be vocal about your request for the blood alcohol test. Even this may not be enough if an officer ignores your requests. To provide verifiable proof of your request, you should write "I want a blood test" on every single document that you sign during the arrest and booking process. This will provide proof of your request as well as the failure of the officer to provide the test in violation of New Mexico law.
Now comes the bad news. It may be pretty difficult finding a blood draw service. Though the law enforcement is supposed to assist in providing a blood test, they may just give you a phone book. Good luck finding someone to come to the jail or substation to take a blood draw, particularly late at night.