He took issue Thursday with Auditor Dave Yost's comment that local officials might have to pay out of their personal bank accounts to mail unsolicited absentee ballot applications.
State law says the secretary of state is the only public official who can do that, but FitzGerald - a Democrat running for governor - has said he might be willing to violate that law.
He said Yost's comments should be interpreted as a threat, and that he should recuse himself from future audits of the county.
"The fact that the auditor of the state of Ohio is saying that public officials who stand up for voting rights are going to be personally financially liable is sending a message to elected officials, county officials all over the state," FitzGerald said, "saying, 'Here's what's in store for you if you do what Cuyahoga County did.'"
Yost made his comment Wednesday to Cleveland.com, and in response to FitzGerald said only that he'd take the county's comments under advisement. Secretary of State Jon Husted has said he will mail unsolicited ballot applications this year statewide.
