Democrats now appear to have at least a three-way primary for the party’s Senate nod in Ohio, where Sen. George Voinovich (R) is retiring in 2010 and leaving a wide-open race for his seat.

State Rep. Tyrone Yates (D), from the Cincinnati area, told local reporters that he has filed the appropriate paperwork to run for Senate. Ohio Secretary of State Jennifer Brunner (D) and Lt. Gov. Lee Fisher (D) had already announced their candidacies earlier this month.

Furthermore, two Democratic Members of the Ohio Congressional delegation — Reps. Tim Ryan and Zack Space — have also been mentioned as possible candidates, but neither has made any overt moves toward running.

The three-candidate primary could give national Democrats a headache in a race that is otherwise viewed as a prime pickup opportunity for party. A bloody primary could hamper the party’s nominee in the general election.

National and local Republicans, meanwhile, are supporting former Rep. Rob Portman. Portman is the only announced GOP candidate, although he could still face a primary challenge from state Auditor Mary Taylor.