Rice said she enjoys her job as treasurer but wants to bring her “experience and track record” to the commission.
“I think the county faces great challenges given all that’s happening with the state legislature and what the federal government is doing to local governments,” said Rice, who was re-elected treasurer in 2016.
Ward said he is running because he wants to bring people together.
“I have no history of being a politician or elected official, but I do believe I can bring a fresh voice rooted in common sense to how we meet the challenges of our community,” said Ward.
Matthews hopes to bring a Republican voice to the all-Democratic commission.
“I still think we need some more business-type leadership,” said Matthews, who stepped down as township trustee in March because he took a project management job with a Cincinnati law firm that did business with Miami Township.
RELATED: Longtime court clerk Greg Brush to retire
Smith could not be reached for comment.
Petitions for the county clerk of courts have been taken out by two people, Clerk of Courts Russ Joseph, a Democrat, and Mike Foley, a Republican who ran unsuccessfully for the job in 2012.
Longtime clerk Greg Brush had been re-elected in 2016 but retired to take a job in Hamilton County. Whoever wins the race will serve out his term, which ends in 2020.
RELATED: Retired Montgomery County clerk of courts takes Hamilton County job
Joseph, was selected by the Montgomery County Democratic Party central committee to replace Brush until the job is filled by someone voters pick in November.
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