PORTLAND — Oregon shed jobs for the second month in the row, though its unemployment rate remained essentially unchanged, the state Employment Department said Tuesday.Oregon’s nonfarm payroll employment dropped by 3,800 jobs in September, following a revised loss of 7,000 jobs in August, according to the monthly jobs report. The late-summer slowdown came after six months of robust hiring, when employers added 42,600 jobs.The jobless rate for September stood at 4.2 percent, up from 4.1 percent in August.The leisure-and-hospitality industry cut 3,700 jobs in September, its second consecutive month of weak hiring after a spike in June and July. State employment economist Nick Beleiciks said employers probably got the workers they needed in early summer and didn’t need as many as the season wore on.Oregon’s construction industry, consistently strong over the past year, added 2,900 jobs. No other industry added half that many.Beleiciks said the forest fires that charred the state in September did not impact the jobs report.“Although some people were out of work because of the forest fires, I don’t think enough people were out of work long enough,” he said. “So, basically, if someone was out of work early in September because of the fires — but they ended up going back to work in September — they’d still be counted as having a job in these figures.”A total of 2.05 million Oregonians were employed in September, an increase of more than 68,000 workers from this time last year, when the jobless rate was 4.9 percent.Another unemployment measure, known as U-6, was at 8.2 percent in September — up slightly from August. The figure includes discouraged workers who stopped looking and part-time workers who want but can’t get full-time jobs.