I'm not sure what you mean by "finished". If you mean you're off probation then the warrant shouldn't have anything to do with your prior DWI. If however, you're still on probation and you have failed to show up for court in MInnesota then you may have a problem and need to double check to see if you missed a court date. If you have, and the warrant is from MN, if the police locate you they might very well hold you in jail until you appear before a judge.
I'm not licensed in WI, but I would assume it's similar there, if you failed to show for a hearing they probably issued a warrant. The key thing is that you have not gone to court when you should have.
Get a lawyer in WI, ask them to figure out what is going on regarding the warrant issue. Good luck.
The situation is not entirely clear from the question as worded. Generally an arrest warrant can only be cleared by getting booked into jail. There are some warrant with a bail alternative, but generally not when there is an alleged probation violation. You can call the appropriate county Sheriff's Office to ask if the warranty has a bail alternative, or is it "body only?"
You should seek help from a DWI lawyer in each state where there is an open case against you.
On a warrant, you can be picked up at any time and jailed until conditions of release can be set. If you retain counsel, often a hearing can be scheduled to make arguments to the court regarding baiul and other conditions of release.
A third offense is extremely serious and, if convicted, is very likely to result in a criminal jail sentence. You should retain legal counsel immediatley.
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