It really shouldn't matter who your attorney is. Either you qualify for a deferred prosecution (DP) or you don't. The biggest advantage of having a private attorney for a DP is he or she will have more time to guide you through the process. Still, if you are motivated you can do the leg work yourself.
Some of the requirements to qualify for a DP are:
(1) You must not have had a prior DP (you only get one in a lifetime);
(2) You must admit that you are an alcoholic and declare that if the alcoholism is treated you believe you will not re-offend;
(3) You must agree to enroll in and arrange for the costs of a two year treatment program;
(4) In most courts the terms of the DP are imposed for five years and include abstaining from alcohol, completing treatment, no new violations, payment of all the costs and whatever other conditions the judge orders.
In general, I don't recomend DPs to my clients. While the prospect of no jail and no loss of license sound very inviting, DPs are usually just a setup for failure down the road. If you violate any of the terms during the five years you can be convicted of DUI without a trial (and you will go to jail and lose your license). If you have had two DUIs in the matter of months you need to consider long and hard whether or not you will be able to complete everything. I'm not saying that no one should ever do a deferred prosecution, but it should rarely be your first option. I'm also not saying you shouldn't enroll in an intensive treatment program if you think you need one. However, in my opinion, it's better to hire a good DUI attorney and see if you have any viable defenses. If not, then you can decide whether a deferred prosecution seems like a good idea for you.
First, a Public Defender is a lawyer. They have to pass the Bar exam and get admitted just like any attorney. Second, Whether or not you qualify for a deferred prosecution has to do with what a treatment agency says about your need for treatment and whether you meet the statutory requirements. I watch Public Defenders help their clients with Deferred Prosecutions on a regular basis.
The answer is yes you can BUT first you have to be deemed an appropriate candidate for the Deferred Prosecution Program. The first step there is to have an alcohol evaluation by a state certified agency and they must deem the person alcohol dependent and amenable to treatment. Assuming that is the case then the reset is really just paperwork where you acknowledge the dangers and benefits associated with the program in terms of successful treatment versus unsuccessful treatment as well as recognizing the rights you are giving up. A public defender should be familiar and knowledgeable with these forms and can certainly handle things.
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