Connecticut added 20,400 jobs in August, while its unemployment rate declined, according to preliminary data released Thursday by the state Department of Labor.

At the same time, the department announced it had revised its original jobs calculation for July up by 5,800, to a gain of 32,300 for that month.

“Connecticut job gains topped 20,000 for the third month in a row,” said Patrick Flaherty, acting director of the labor department’s Office of Research, said in a statement. “However, the pace of gains has slowed after the 77,300 June increase. The largest August job gains were in health care and social assistance, leisure and hospitality and trade and transportation. Federal government also gained due to the decennial Census.”

Connecticut’s unemployment rate in August was officially 8.1 percent, down 2.1 points from July. But there are a number of issues with the calculation of that rate, and labor department officials estimate the actual rate in mid-August to have been in the range of 14 percent to 15 percent.