Clark County’s labor market report for January, including payroll and unemployment figures, is slated for release on March 11.SEATTLE — Washington state has more jobs than before the start of the recession, with a January unemployment rate of 6.4 percent, the Employment Security Department reported Wednesday.Washington added 3,800 jobs between December and January. State economists say they now believe Washington didn’t lose as many jobs as originally thought and has more than recovered from recession job losses. Previous data suggested the state lost about 205,000 jobs from February 2008 through February 2010. After further study and analysis, economists now believe the losses were around 189,000.A recent statistical update also found Washington had gained more jobs last year than previously announced, resulting in a net job growth from February 2010 through January 2014 of nearly 193,000 jobs.State officials say the strongest growth was in private sector jobs. Over the past year, the private sector has added 58,700 jobs, while government jobs have grown by an estimated 2,700 jobs.The January 2013 unemployment in Washington was 7.3 percent.Washington’s unemployment rate rose as high as 10.2 percent at the start of 2010 but has been falling steadily ever since. The state says some 222,000 people are still looking for work.