Contact your attorney.
David B. Snyder, Esq.
6876 Buckley Road
Syracuse, NY 13212
Mr. Snyder is licensed to practice in New York and does not offer legal advice in other states. This answer is meant to be a public service and not an attempt to solicit business. Moreover, my answer cannot be considered a legal opinion of your case / inquiry. Unless I am retained in a matter and have completed a full investigation of the underlying facts and law, I cannot give an opinion on which to rely. Furthermore, unless your matter concerns New York law, I am not licensed to practice or give specific legal advice in your state.
Whether the Michigan Court tries to "find" you after you missed your show cause date depends on your overall criminal history. For example, if this is your only criminal offense in your lifetime, and you now live in Arizona, it is EXTREMELY unlikely the Michigan Court will attempt to have you "picked up" in Arizona on an open warrant. However, your Michigan driving privileges may be affected, and this could in turn affect your Arizona driving privileges. I would kindly but strongly recommend you consult with a Michigan Drunk Driving Specialist to asses all your options. "Cleaning up" all your open Michigan Court issues may prove better than having your new state's driving privileges suspended. I wish you all the best of luck. Warmest regards, Matt Catchick.