"Don't leave the state" is a common condition of probation in felony cases. Soemtimes, it is as well in misdemeanor cases. A condition of probation must be announced by the judge at the dispositional (sentencing) hearing, and is often clarified in writing as well. You can look at those. If it is a condition, you can contact the probation office of the court to inquire. Even when it is a condition, probation officers will often authorize it, or recommend a judge allow it, assuming all conditions requiring action have been completed. You may wish to complete all of those conditions, then contact a probation officer to discuss.
Your question is a little confusing because you state that you're on UNsupervised probation, yet you are still required to attend some classes. Usually a judge will sentence you to supervised probation when you still have classes left to attend, so you might want to double check and make sure your probation is truly unsupervised. Even if probation isn't actively meeting with you, your probation could still be a supervised probation. This makes a big difference in how I would answer your question. If probation is UNsupervised, you are free to leave the state as long as you continue to meet all of your conditions. You may even be able to complete a comparable class in Texas to fulfill that obligation. If probation is supervised, you should seek permission from probation before you move. Typically probation needs about 3-6 months of advance notice to transfer your probation, so tell them immediately if your probation is supervised.
As for your driver's license, you won't be able to get a new valid license in Texas until you get valid with Minnesota. In the meantime, you might be able to apply for a Texas state ID, but that might even be problematic because you're still revoked here in Minnesota. You should complete whatever license reinstatement requirements you have left to do before you leave here (such as paying the reinstatement fee and passing the written DWI test).
I agree with my colleagues. You may be able to have your probation transeferred to the State of Texas. However, you should be absolute certain as to the nature of your probation before you make any moves. If you are following the terms of your sentence, thsi is good, but if you still have "hoops" to jump through, I would make sure to get this straight asap.
You will probably have to take the appropriate steps with the MN DPS to get your driver's license back before you can get a valid license in another state.
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Everything my colleagues said is correct. I add this: Usually a "don't leave the state" condition is NOT included in a non-Felony (misdemeanor or gross misdemeanor) sentence as you have. That being said, you will need to double check your paperwork. In any case, non-felony probation will NOT be transferred to another state, so you would still be on probation here, but would be living in another state, which is fine as long as you do not have to attend monthly probation meetings, etc, in Minn., which you should not have to do, certainly not after you have completed all the conditions of your sentence such as attending classes. The other possibility is that IF you have completed all your probationary conditions then your PO may terminate your probation early at the time you leave for Texas, knowing that having you on probation here while you are permanently in TX is relatively meaningless.