L.A. County’s unemployment rate fell to another new low of 4.5 percent in April, but in a sign that the local economy is close to full employment, employers in the county reversed their hiring trends and shed a net 7,000 jobs last month, state figures released Friday show.

The county’s unemployment rate, which in March hit 4.6 percent, its lowest level in more than 40 years, fell again in April to 4.5 percent as 24,000 more residents surveyed reported they were working, the state Employment Development Department reported. The county’s total labor force grew by 19,000 to 5.1 million.

“We are in a full-employment environment,” said Genine Wilson, vice president of the Southern California division of Kelly Services, a Troy, Mich., staffing firm.

The statewide unemployment rate fell to 4.8 percent in April, while the national unemployment rate was 4.4 percent. The rates in the county’s two largest cities, Los Angeles and Long Beach, were 4.4 percent and 4.5 percent respectively.

But the good news ended there. Payroll jobs in Los Angeles County fell by 7,300 to 4,436,100 in April, led by drops in professional/administrative/support services, local government, and the entertainment sector. Gains in leisure/hospitality and construction jobs were not enough to offset these declines.

What’s more, the rate of year-over-year payroll job growth, the most closely watched figure among local economists, slowed in April to 1 percent as about 45,000 jobs were added. That’s about half the year-over-year job growth rate the county was experiencing a year ago.

Wilson said she’s seeing the slowdown among her employer clients.

“Companies in most sectors that we place have reached capacity in terms of the number of positions they have open,” she said. The exceptions: health care and information technology support.

Also disappointing is a dramatic drop in jobs in the region’s marquee sector: entertainment. The motion picture and sound recording industry shed 4,700 jobs between March and April and a whopping 13,000 jobs in the 12-month period ended April 30, which represented an 8 percent year-to-year drop, making it the biggest job-losing sector.

This all comes despite the string of upbeat announcements from local elected officials and industry trade groups about the positive impact that the state’s film tax credit program is having in getting jobs to return to the region.

Several studios have announced significant job cuts in recent months, including Walt Disney Co., Paramount Pictures Corp., and NBC/Universal. But Wilson said other factors may also be at play, including a shift in the industry away from full-time payroll employment towards more “gig economy” contract work and a shift away from big-budget films locally with huge casts and crews towards more low-budget projects.

Public policy and energy reporter Howard Fine can be reached at [email protected]. Follow him on Twitter @howardafine.