Track live results for tonight's Primary Election as they come in Ohio Secretary of State New design for Ohio's "I Voted" sticker, created by 12th grader Emily Legg. and last updated 2021-05-04 23:29:16-04 CLEVELAND â The polls in the May 4 Primary Election in Ohio close at 7:30 p.m. Among the issues up for vote during this relatively small election are several tax levies for local districts. School districts are hoping their communities help save their schools as some like Parma City Schools are desperate after failed levies over and over. The state also rejected money to patch up their problems, forcing them to start over with new construction.