The unemployment rate in the Buckeye State fell from 4.2 to 4.1% in the month of May.There were 239,000 Ohioans out of work last month, that’s down 8,000 from the April report.But employment in Ohio also fell in May, with job losses reported in construction, financial services, and health position.Gains were posted in manufacturing jobs during the month of May.The U.S. unemployment rate for May was 3.6%.County by county jobless numbers for Ohio will be released on Tuesday afternoon.