Los Angeles County’s job picture was mixed in May, the state’s Employment Development Department said Friday. The county’s unemployment rate edged up to 12.3 percent from 12.2 percent but 6,500 payroll jobs were added.

The county’s unemployment rate rose in May as nearly 40,000 fewer residents reported having jobs than in April. The unemployment rate is a full percentage point higher than May 2009.

These figures run counter to state and national trends. The statewide unemployment rate edged down to 12.4 percent in May from 12.5 percent, while the national unemployment rate also decreased slightly to 9.7 percent.

The county’s two largest cities, Los Angeles and Long Beach, continued to post higher unemployment rates than the countywide average, at 13.4 percent and 13.3 percent respectively.

The news was a little more encouraging on the more closely watched payroll jobs front.

L.A. County added 6,500 non-farm payroll jobs in May to reach 3,790,100 jobs, an increase of about 0.2 percent. But, when adjusted for seasonal factors, the county only added about 600 non-farm payroll jobs in May, according to Beacon Economics.

Federal government hiring of temporary census workers was a major factor in the increase, but there were also increases in food services and the information sector, which includes motion picture production.

Private education lost jobs in May as the school year began winding down. Professional and scientific services also lost jobs.

Meanwhile, the year-over-year payroll jobs trend continues to show some improvement. About 70,000 non-farm payroll jobs were lost between May 2009 and May 2010, a drop of 1.8 percent. But that’s an improvement from the 83,000 year-over-year job loss recorded in April and is less than half the figures from a year ago.

The motion picture industry was by far the biggest gainer in the past year, with an increase of 23,000 jobs.

But most other industries continued to record year-over-year job losses, including manufacturing – which shed 22,000 jobs – wholesale and retail trade, construction and professional and business services.