Yes, but whether or not you get a private lawyer or a public defender, you SHOULD have a lawyer for the criminal court process as well. In fact, not having a lawyer for your criminal case might hurt your DMV hearing which could make the DMV hearing a waste of time. Feel free to ask more questions on the phone at 818-500-0678.
That is absolutely possible. Though it depends on the attorney how much they charge. Usually it is better to have the same lawyer handle both cases since much I the prep work for a dmv hearing will transfer to the court case well, include investigation if the case and cross-examination of the officer or lab analyst.
Some lawyers will only take a case if doing both, most, however, would be fine with splitting the two cases if that is what you wish to do. Contact some DUI attorneys from Avvo.com or look on the CA DUI Lawyers association site to find some.
Contact a few to consult with and get fee information. I would suggest you strongly consider the overall value and experience of the lawyer you wish to hire, and not just fees. That way, you can ensure you hire someone whom you believe will give you the best chance.
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You can absolutely get a lawyer solely for the DMV hearing if that is what you want. I would recommend calling around to see if someone can represent you for both hearings for a reasonable price though. I would not represent yourself during the court hearing if I were you. My office is in Diamond Bar and I would be more than willing to discuss your case with you in further detail for no cost. However you proceed i wish you luck!