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DENVER—Colorado’s unemployment rate rose one-tenth of a percentage point to 3.6 percent in May as a sluggish housing industry forced construction job losses, a state labor official said Tuesday.

Businesses eliminated 1,400 jobs in the construction industry last month, the Colorado Department of Labor and Employment reported. About 4,200 jobs have been lost since May 2006.

The May jobless rate compared with 3.5 percent in April and 4.5 percent in May 2006, according to the department’s monthly report. The nation’s unemployment rate was steady at 4.5 percent in May.

Colorado’s nonagricultural workforce was about 2.32 million in May. Six industry sectors reported job gains, including professional and business services, financial activities, education and health services and information, according to the department’s seasonally adjusted statistics.

Besides construction, sectors recording job losses included manufacturing and leisure and hospitality, the statistics showed. One category, other services, was unchanged.

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