Connecticut added 600 jobs and its unemployment rate dropped three-tenths of a percent to 5.7 percent in June, according to the Labor Department’s report released Monday.

“Above trend private-sector job growth looks to be continuing, while the jobless rate has recently declined significantly,” Andy Condon, director of the Labor Department’s Office of Research, said. “Connecticut’s unemployment rate, which is below 6 percent for the first time since August 2008, has not been this low since July 2008.”

CBIA economist Pete Gioia said while the unemployment rate is the lowest since July 2008, it’s still more than a percentage point higher than neighboring Massachusetts.The U.S. unemployment rate is 5.3 percent.

“Still higher than most of the other New England states,” said Gioia, “and shows just how stubborn our economic recovery is more than five years after the end of the recession.”

Gov. Dannel P. Malloy put a more positive spin on the numbers.

“This is yet another milestone reached — unemployment is down to its lowest point in seven years,” Malloy, said. “This news comes just a month after we created nearly 6,000 jobs, a huge one-month total. We are no doubt making progress, and our strategy is no doubt moving Connecticut forward.”

However, the May jobs gains were not as big as initially reported. The Labor Department reported last month that the state added 6,400 jobs, but those numbers were revised downward by 500 to 5,900.

The Labor Department numbers show the state has increased its total non-farm jobs by 27,000 over the year.

Connecticut has now recovered recovered 97,900 positions, or 82.3 percent of the 119,000 seasonally adjusted total nonfarm jobs that were lost in the state during the March 2008-February 2010 employment recession. Connecticut’s jobs recovery is now in its 64th month and is averaging about 1,530 jobs per month since February 2010.

The private sector has recovered employment at a faster pace (about 1,644 per month) and has now replenished 105,200 (94.3 percent) of the 111,600 private sector jobs that were lost during the employment downturn. The state needs to reach the 1,713,000 job level to enter a nonfarm employment expansionary phase.

Out of the state’s 10 major industry sectors, four posted employment gains. Construction and mining showed the greatest increase at 3.9 percent followed by the financial super sector, manufacturing, and professional and business services.

Government posted the largest decline in June, followed by leisure and hospitality; trade, transportation, and utilities; and education and health services. The information super sector was unchanged.