L.A. County’s unemployment rate continued its rapid descent in April, falling to its lowest point in nine years.

The drop to 5.1 percent came as employer payrolls in the county gained nearly 16,000 jobs, according to state Employment Development Department figures released Friday.

The biggest increase in payroll jobs last month came in motion picture/sound recording (up 4,700 jobs), a further sign that the state’s bigger tax incentives for filmmakers may be having their intended effect of boosting local jobs. No industry sector posted a significant net drop in payroll jobs last month.

For the first time in recent years, the county’s unemployment rate was lower than the statewide rate of 5.3 percent and is now virtually equal to the rest of the nation, where the rate last month remained steady at 5 percent.

Last month’s figures showed another milestone: the unemployment rate in the city of Los Angeles was 4.9 percent, dipping under 5 percent for the first time in nine years.

Over the past year, the county has gained nearly 107,000 jobs for a very strong year-over-year growth rate of 2.5 percent. That rate had been hovering at just under 2 percent in recent months.