Found this on the net from the Columbus Dispatch:
In a statewide election, the margin of defeat has to be onequarter percent or less for an automatic recount. That would be 10,000 out of 4 million votes cast. Otherwise, a recount could be triggered by suspicion of irregularities by the losing candidate.
Here's how a recount works in Ohio:
After the secretary of state certifies the final official count, a challenger has five days to ask for a recount, and the recount must start within 10 days after that. A recount may be requested in any county and for any precinct. Representatives for each candidate may witness the counting.
If a candidate contests the election, the complaint is heard by the chief justice of the Ohio Supreme Court. Any appeal is heard by the entire court, which has the final say.
Kent Markus, associate professor of law at Capital University, said, "We're in pretty good shape regarding our ability to do a recount."
Markus has had personal experience. He was Fisher's chief of staff in the attorney general's office and went through the 1990 recount. He said many of the mistakes involve simple mis-recording of votes taken from the voting machines rather than conspiracy theories "that make everybody nervous and suspicious."
To avert a hanging-chad controversy, the legislature passed a law in 2001 specifying how punch cards, used in the majority of Ohio counties, are counted. If a chad is attached by three or four corners, it is not counted.
Terry Casey, a Columbus political consultant familiar with voting-machine technology, said electronic-voting machines have five separate memories, a paper tape and an image on the machine to preserve the vote. "There's a master count on each machine," he said.
Pfeifer agreed that Ohio's law is "pretty good" on recounts but said any defeated candidate appealing the results probably would be better off in federal court than in state court.
"Our court is loath to do much of anything with election disputes," said Pfeifer. "The (case law) is very unfriendly." Pfeifer said if an appeal is based on an institutional error, "if you didn't attempt to dispute it and get it fixed before the election, tough luck."
lleonard@dispatch.com
Also found, http://moritzlaw.osu.edu/electionlaw/docs/171-7a-state-hava.pdf
Which is Ohio's plan for implementing the Help America Vote Act of 2002, which says
Anyone who feels his or her voting rights have been violated has a right to file a written complaint, to have it heard by the secretary of state within 20 days and have a decision within 60 days.
Oh, lovely, then it goes on to say that the remedy can't be monetary and can't be changing the results of an election. So I don't know what the hell good that goes, except that we can at least raise hell with it.