L.A. County’s unemployment rate dropped slightly last month to 12.4 percent as teachers and other school personnel returned to work and local governments also increased their hiring.

September’s seasonally adjusted rate compared to a year-earlier rate of 12.9 percent and August’s 12.5 percent, according to state figures released Friday.

Based on unemployment rolls, the state Employment Development Department said employment in the county increased by about 10,000 people to 4.25 million over the month, while the number of unemployed people fell by 1,000 to 602,000.

In separate statistics supplied by employers, educational and health services led all industries with a year-over-year job gain of 14,500, split between educational services primarily at colleges, universities, and professional schools, and health care and social assistance. It’s the third consecutive month that the sector has led in yearly gains.

The government sector added a net 10,200 jobs during the month, with a 12,300-job gain in local government – mostly in K-12 educational services – offset by declines in state and federal hiring.

In the private sector, the information sector added 7,600 jobs, mostly in motion picture and sound recording hiring. The hospitality industry gained 7,300 jobs and the professional and business services sector gained 3,100.

Construction saw the largest decline, down 3,900 jobs, most of that coming from the specialty contractor segment. Other industries seeing declines included financial, manufacturing and transportation.

Statewide, September’s unemployment rate was 11.9 percent, down from 12.5 percent a year earlier and 12.1 percent in August.