Below is the information I received from OHS:
The Ohio Revised Code legally describes the Ohio State Motto below:
Section § 5.06. State motto.
General Assembly: 103rd
Bill Number: S.B. 193
Effective Date: 10/1/1959
"With God, All Things Are Possible" shall be adopted as the official motto of the state.
The following information about the Ohio State Motto describes the changes that have been made to it. The booklet from which this discussion comes was published in 1968.
Hatch, Margaret G., Ohio's Official Symbols: Their History and Significance. Columbus, OH: Ohio Historical Society, 1968.
Ohio has had two state mottoes during its history. The first was devised during the aftermath of the Civil War; the second in 1958 from a youngster who had turned to the Bible as the source of his inspiration.
Jacob D. Cox became governor in 1866. He had been superintendent of schools and an attorney in Warren, and had served as a general during the Civil War. At the close of the conflict and upon his election as governor, Cox and many in the Republican party wanted to express their pride in the prominent role Ohio had played in defending the Union cause. The war had stimulated Ohio industry and commerce, and Cox and his party were confident in the state's future in spite of the dissensions within their ranks. Remembering that inadvertently the legislature in 1805 had repealed the law which had specified the design of the Great Seal of the state of Ohio, Republicans, with the support of Governor Cox, passed a law on April 6, 1866, specifying a new design for the Great Seal which incorporated a new state motto: "Imperium in Imperio," an empire within an empire.
A furor arose over the new law which Governor Cox had promptly implemented with a proclamation. The criticism, coming primarily from Democrats, was that the motto was too pretentious, regal, and imperial to be associated with a democratic state. Besides it was in Latin.
The critics would soon have their day in Senate and House. The election of 1867 swept a Democratic majority into the legislature and at the same time saw the resounding victory of the Republican candidate for governor, Rutherford B. Hayes. Detractors of the motto soon laid plans to repeal the great seal law, with it abolishing the motto, and return the Great Seal to its original design as prescribed in 1803, without a motto. State Representative Ralph Leete of Lawrence County sponsored the act of repeal which was adopted. Governor Hayes cold do nothing even if he had wished to; governors did not then have the veto power. For the next ninety-one years, Ohio was without a motto, official or unofficial.
In 1958, Jimmie Mastronardo, a twelve-year-old student in the sixth grade at Cincinnati's Hartwell School was concerned that Ohio among all the states had no motto. His teacher had pointed out the fact in Ohio history class, and Jimmie resolved to do something about it. With the help of his parents, Mr. and Mrs. John Mastronardo, 1814 Avonlea Avenue, he found what appeared to be an ideal state motto in Matthew 19:26: "With God all things are possible." Attributed to Jesus, the words were used to explain to the disciples His statement that "It is easier for a camel to go through the eye of a needle, than for a rich man to enter into the kingdom of God." Jesus, according to Matthew, then said by way of explanation, "With men this is impossible, but with God all things are possible."
Jimmie reported his suggestion to the class. It was immediately accepted and a petition was circulated by the teacher and interested friends. State Senator William H. Deddens of Cincinnati introduced a bill in the legislature early in 1959. With the bipartisan assistance of the State Representative A. G. Lancione in the House, the bill had clear sailing, particularly since Jimmie was called to testify before appropriate Senate and House committees. Appearing again in support of the bill, Jimmie addressed the House of Representatives from the speaker's desk before the final vote was taken. Governor Michael V. DiSalle signed the bill into law on July 2, and it became effective on October 1, 1959.
The following information is taken from Columbus Dispatch newspaper articles written on April 26, 2000, March 17, 2001, and June 8, 2001.
In April 1996 Governor George V. Voinovich suggested that the Ohio State Seal and the State Motto be inscribed on the Ohio Statehouse grounds. This touched off a debate that the motto should not be used by Ohio in any official way because of its biblical origins. On September 30, 1997, the ACLU filed a federal lawsuit on behalf of Reverend Matthew Peterson of Cleveland asking that the Ohio Motto be declared unconstitutional. U.S. District Judge James L. Graham ruled in September 1998 that the state could use the motto, but officials were prohibited from citing Matthew 19:26 as the source of the text. A three member panel of the 6th U.S. Circuit Court of Appeals in Cincinnati ruled on April 25, 2000, that the Ohio Motto was an unconstitutional endorsement of religion. The decision was appealed to the full panel of the 6th U.S. Circuit Court of Appeals. In a 9-4 decision, the 6th U.S. Circuit Court of Appeals ruled the motto was constitutional on March 16, 2001. Judge David A. Nelson, who was part of the majority, stated, "Just as the motto does not have as its primary purpose the advancement of religion, it does not have the primary effect of advancing religion either." The ACLU announced in June 2001 that it would not appeal the decision to the U.S. Supreme Court. As a result, Ohio's State Motto continues to be "With God, All Things are Possible."
Okay, I admit, the first motto sounds, well, goofy to me. Seriously. The last thing we need is to suggest America is an Empire, and Ohio is hardly an empire either. New York can go ahead and be that arrogant if they wish, but Ohio? Farmers and steel mills? So, I can't say I'm sad to see that go, but we didn't really need one once we got rid of that one, and as bad as the old one was, that hardly justified replacing it with one that makes claims about a god I don't believe in.
I was interested to see that the ACLU did not take the state motto case to the US Supreme Court. Based on their rulings in similar cases, I doubt it would have made much difference, but by quitting where they did, the case is only a precedent in 6th Circuit, and not nationwide, leaving the door open for other challenges of other state mottos. It's a shame that something so obviously Biblical did not raise more red flags, however.