Yes you can reschedule, but I suggest you have names of attorneys you have consulted so the judge knows you "good cause" in requesting the continuance. Many of us on Avvo offer free consultations.
My colleague is correct. You can postpone, but your likelihood of success to show good cause will be to show that you are not just interpolating delay, but that you have a very good reason for requesting it. You will not have to explain the discord between you and your attorney in any detail. So, do not volunteer it. When asking for the additional time, indicate that you plan to have substitute counsel and have a few in mind to quickly interview and then to retain one. There are several good options here. www.taubcriminaldefense.com
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If you have someone in mind, have you talked to him or her? Having the names of several attorneys is fine, but I suspect the judge may ask if you have talked to any of them. Do you have any co-defendants or are you by yourself? Easier to get the preliminary hearing continued if by yourself. Have you told your current attorney of your plans? If you have, your attorney can call the DA so the DA can call off her witnesses so they don't show up. If the DA is ready and has her witnesses, the judge may not be willing to continue the preliminary hearing.
You can postpone your preliminary hearing even without good cause by waiving time. Although many attorneys think this is the wisest course of action it does mean you may wait a long time in custody without a preliminary hearing being scheduled. In a homicide case this is desirable; in most other cases it is not.
If you have a new attorney in mind, he or she can substitute in at the time set for prelim and the judge will continue the hearing so your new attorney can review the file and prepare.
Call me if you are looking for representation and wish to discuss your case.
You should consult/hire a new attorney before the date. He or she can then substitute in and save you the hassle of dealing with asking for a continuance.
The above stated is advice only, and does not establish an attorney-client relationship.