L.A. County’s economy improved in February as the unemployment rate dipped to 10.3 percent and the county added 39,000 jobs, according to state figures released Friday.

The unemployment rate returned to 10.3 percent in February after rising slightly in January to 10.4 percent, according to figures released by the state Employment Department. The rate has fallen considerably from 11.4 percent a year ago.

Nonetheless, the local unemployment rate remains higher than the 9.6 percent February statewide average and well above the national 7.7 percent average.

Locally, the county’s two largest cities, Los Angeles and Long Beach, posted unemployment rates of 11.4 percent and 11.3 percent, respectively.

The picture was a bit brighter on the payroll jobs front. After losing a whopping 81,000 jobs in January following an annual data revision, L.A. County gained roughly half those jobs back in February, posting an increase of 39,000 to reach 3.9 million jobs.

The payroll jobs figures are taken from periodic surveys of employer payrolls, while the unemployment figures are based on a sampling of household surveys.

Hollywood employment rebounded as the motion picture industry gained 15,700 jobs last month. That was followed by a gain of 10,500 jobs in professional and business services. Private education and health services gained 6,700 jobs. All three sectors took big hits in January’s data revisions.

Retail trade suffered the biggest loss, dropping 5,000 payroll jobs in February.

The picture is even better for the closely watched year-over-year payroll jobs figures. When taking last month’s total compared to the February 2012 total, the county gained roughly 90,000 jobs, for a growth rate of 2.3 percent. That’s the fastest year-over-year growth rate since the recession began in late 2007.

The biggest gain was in professional and business services, which added 25,300 jobs. The leisure and hospitality sector gained 21,000 jobs. Government payrolls posted the biggest losses, down by nearly 10,000 jobs.

Brandi Britton, Los Angeles area district manager for Robert Half International, a Menlo Park staffing firm, said she has seen demand for workers pick up steadily over the last several months. She also noted that roughly one-third of the workers her company places are now being asked to stay on full-time, up from less than 10 percent a couple years ago.

“What we’re seeing now is that with employers showing more confidence in the economy, they are more likely to ask their temporary hires to stay on full time,” Britton said. “We’ve been waiting for this to happen for quite some time.”