There are a number of factors at play when you consider an appeal after a guilty plea, and all of them depend on more facts than you've stated here. If your son hasn't consulted an experienced lawyer who does criminal appeals, he should do so immediately. There are often very strict deadlines that, if missed, would make it virtually impossible for him to appeal his conviction.
The primary issue is whether your son has waived his right to appeal. In most circumstances, your son likely has waived his general right to appeal his guilt by pleading guilty. There are generally a few exceptions -- he can probably appeal on the grounds that he had ineffective assistance of counsel, the plea was involuntary, or their was prosecutorial misconduct. And it's unclear from what you've said here that any of those circumstances might be the case here. (They're probably not.)
Again, if you want to pursue this route, you should contact an appellate lawyer ASAP.
Nothing in this communication should be construed as creating an attorney-client relationship. I provide this service for educational purposes only. I will take no action on your behalf unless you have hired me and a written retainer agreement is signed. I am licensed only in Tennessee and California, I strongly suggest you consult with an attorney in your city and state as Statute of Limitation and other deadlines can limit your recovery or affect your legal rights.
First, since the police requested a blood sample for his DUI arrest, he would not have been charged for the blood test.
Second, in NH, the police determine what type of chemical test to request of a person suspected of DUI. Failure to submit to the blood test will be considered a refusal. His willingness to take a urine test that is not offered to him is not a defense.
Finally, if your son pled guilty to DUI, he cannot appeal his guilty finding simply because his breath results were 0.0. If he wants to attempt to withdraw his guilty plea to the DUI, he should speak with an experienced criminal defense attorney.
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