L.A. County’s job creation machine slowed in December as the unemployment rate remained stuck at 10.2 percent and job payrolls grew by less than 10,000, according to state figures released Friday.

The unemployment rate, which had been falling steadily throughout 2012, was unchanged last month from November at 10.2 percent, according to figures from the state Employment Development Department. However, that was well down from 12 percent the year before.

The rate was higher than the statewide average of 9.8 percent for December (also unchanged from November) and way above the national average of 7.8 percent.

Locally, the unemployment rates in the county’s two largest cities – Los Angeles and Long Beach – rose slightly to about 11.2 percent in December from 10.8 percent in November.

Nonfarm payroll employment rose by 9,600 jobs in December to reach 3.92 million. The growth rate of 0.2 percent was the most sluggish in several months. Adjusting for seasonal factors, the county actually lost 2,000 payroll jobs, according to Los Angeles consulting firm Beacon Economics.

“Employers were definitely less confident in making permanent hires in December because of fears of the fiscal cliff,” said Jodi Chavez, senior vice president in Los Angeles for New York-based Accounting Principals, a staffing firm. “They didn’t know how much their cost of doing business would go up because of tax changes.”

The largest gain came in construction, which rose by 2,500 jobs. Next were the trade-related activities of transportation and warehousing, which rose by 2,400 jobs. Motion picture and sound recording, which has seen steady growth over the last year, increased by 2,200 jobs.

Retail trade, which normally spikes in December with last-minute seasonal hiring, was flat in December. The largest declines came in non-profit organizations (down 1,900 jobs) and manufacturing (down 1,000 jobs).

Robert Kleinhenz, chief economist for the Los Angeles County Economic Development Corp., said the sectors showing declines were also hit with fears over program cuts from the federal government as a result of the fiscal cliff negotiations.

The unemployment figures are derived from a household survey. The payroll jobs data come from a sampling of local employer payroll filings with the state.

Despite the sluggish monthly gains, the county’s jobs picture did show significant improvement during the past year, with about 70,000 jobs added for a growth rate of 1.8 percent. The largest gain was in accommodation and food services, which rose by 18,000 jobs. The manufacturing sector posted the biggest drop, shedding 6,000 jobs.