Thereâs more positive news on the Ohio jobs front. The latest unemployment report from the Department of Job and Family Services lists a May jobless rate of 7.3 percent. That's down from 7.4 percent in April and marks the tenth-straight decline in Ohio unemployment. In a separate survey, the state added 19,600 jobs in May. The jobs gains came across sectors, with professional and business services adding about 4,500 jobs, 6,000 new jobs in manufacturing, and nearly 6,000 position in private education.