UPDATED: Copy of the complaint with case number available here.
Jason at DarkeGOP posted this ruling first and has excerpts from the ruling here.
Having read the first 15 pages of the ruling, from the entire 6th Circuit U.S. Court of Appeals, I call the majority opinion decision 'scathing.' They decide that Jennifer Brunner, Ohio's Secretary of State, made claims she could not support in saying that implementing the ruling of the lower court would be too difficult this close to an election. They also write that she tried to straddle two aspects of the law in order to support her position. They document that she had been verifying the information and sharing it with local boards, but that she stopped doing so. Considering that aspect, they decide that to do so again would not be burdensome.
They rule there is no attempt in verifying voter registrations to prevent people from voting, but that sharing voter identification mismatches with the local boards of election will only give the local boards the ability to pursue better, more accurate information from voters who have recently registered.
Also, I understand that Brunner announced today that she would voluntarily follow the law, apparently expecting the ruling of the court to go against her.