Would I need to write turn in expungement papers in person to courts although I now live in another state?

Before you expunge a case, you need to pay all fines and perform all terms of your probation. Restitution is one of those terms. Think of the logic behind expungement and you can answer your own question. If you have not "paid for your 'crime'", (in your case the DUI), both actually and figuratively, how can you get it wiped off your record. Restitution is a way to literally pay for your crime. So the answer is yes, you 'need to completely pay your restitution'. As for the actual mechanics of petitioning the court for expungement, in some divisions of some courts in California you can mail in expungement petition request, once you pay the restitution, and the court will rule of it without you having to appear. In others, while you can mail in the expungement petition request, you have to actually appear in person before the court will issue a decision.