In what was one of the 2012 election cycle's most important battleground states, "voter fraud does exist," Ohio Secretary of State Jon Husted acknowledged in a report on Thursday. "But it is not an epidemic."

Husted, a Republican and the state's chief elections official, said at a news conference and in an accompanying report that based on a survey of all of Ohio's 88 counties conducted in the wake of last November's election, 625 possible voting irregularities were reported across the state and 135 of them have been sent to law enforcement for further investigation.

Of the 135 investigated instances of fraud in Ohio, a state where President Obama beat Mitt Romney by some 166,214 votes, 20 of them involved voters who cast ballots in both Ohio and another state and will be referred to the Ohio Attorney General.

"Our effort to look into irregularities and root out voter fraud sends a strong message that no amount of fraud is acceptable," Husted said in a statement. "If you cheat, you will be caught and held accountable."

Other "irregularities" that surfaced in the post-election survey included double voting, standing in for another voter, and voting from an address from which an individual was not eligible, according to the secretary of state's report.

Before Election Day in 2012, a federal judge blocked new voting laws proposed by Ohio Republican lawmakers that were aimed at reducing voter fraud by restricting early voting. Ohio requires voters provide proof of identity at polling places such as a driver's license, bank statement or utility bill.

No instances of voter suppression were reported. In Ohio, more than 5.6 million ballots were cast in the 2012 election.

The results of Ohio's review come on the heels of President Obama's appointment of members to his Presidential Commission on Election Administration earlier this week. The commission is tasked with identifying ways to solve the problem of long lines and inefficient polling locations during the 2012 election. Members of the commission include former top lawyers for both the Obama and Romney campaigns.