Employment data compiled by the U.S. Bureau of Labor Statistics said Connecticut’s unemployment rate was at 9 percent for the month of August, up from 8.5 percent in July. That’s the largest monthly increase in the rate since 1976, when current methodology was established.

The report indicating Connecticut lost 6,800 non-farming jobs between July and August has state officials scratching their heads trying to square the figure with other data like unemployment claims.

In a press release, Labor Department Research Director Andy Condon said, “to date we can find no corroborating evidence that the record losses in employment and increases in unemployment, indicated by the household survey, are occurring at this magnitude.”

According to the report, Connecticut’s jobless rate was higher than the national average of 8.1 percent in the month of August.

The report cites steep losses in the private sector, which it said lost 6,300 jobs. Many of those jobs were in the leisure and hospitality supersector which lost 3,100 jobs.

Gov. Dannel P. Malloy released a statement questioning the accuracy of the numbers. The state has not seen a rise in the number of people seeking unemployment benefits for the first time, he said. The number actually dropped slightly from July when it was 4,602 to August when it was 4,779. Malloy said tax withholdings rose 3.6 percent after adjustment.

“Those two trends are the opposite of what you would expect to see if the state was losing jobs at the rate suggested in this report,” Malloy said.

Still, the governor said he was well aware the state faces strong headwinds both nationally and internationally.

“We’ve also recently learned that the recession was far worse than we thought and had a far deeper impact than we understood at the time. And I’ve said time and again that we’re not going to reverse 22 years of job stagnation in 20 months,” he said.

House Republican leader Lawrence Cafero issued a statement calling Malloy’s response to the report an effort to spin the numbers. The administration never looks for “corroborating evidence” when the news is good, Cafero said.

“If Gov. Malloy is going to take credit for success then he must also admit when he has not succeeded. And this is that time,’’ Cafero said.

Cafero told reporters he hoped voters were paying attention to the negative employment trend, something he said stemmed from bad policies resulting from years of Democrats controlling the legislature.

“Give us a shot. Vote Republican,” he said, standing outside the state Capitol.

Roy Occhiogrosso, Malloy’s senior communication adviser, said Republicans controlled the governor’s office for the last 16 years.

“During which time we grew exactly zero jobs. So for 16 years there was no discernable economic development strategy in this state. After 16 years of driving the car into the ditch, now he’s blaming the guy dragging the car out of the ditch?” Occhiogrosso said.

Occhiogrosso said the alternative budget proposed by Republicans last year would have made unemployment numbers worse.