You can read the complaint this this link. It raises only state law issues, and reserves the right to bring the federal issues back to federal court. Notably, the complaint fails to allege anything about the vote counts, which it seems to me could moot Miller’s claim (because even if none of the ballots Miller objected to were counted, Murkowski still should have more votes than Miller). This article in the Anchorage Daily News explains that the federal law barring certification now kicks in for the duration of the state suit, and could result in there being a period where Alaska would be represented by only a single senator.