By Peter Rudegeair

Nov 2 (Reuters) - Demand for legal services in the United States fell for the second consecutive quarter, according to data compiled by the Peer Monitor Index.

The index, which measures change in the factors affecting law firm profitability, including billing rates, demand, productivity and expenses, is a Thomson Reuters product.

Billable hours for the industry ticked down 0.8 percent in the third quarter, compared to the second quarter's 0.2 decline, according to the index.

There was waning demand for all practice areas except labor and employment, which grew 2.5 percent. Demand for corporate work was down 1 percent, while demand for litigation fell by 1.3 percent in the quarter.

Geographically, New York was the report's lone bright spot, with billable hours up 4 percent in the third quarter. Los Angeles, Silicon Valley and Washington all posted 2 percent declines, and Chicago was down 3 percent.

Firms' direct expenses rose 3.5 percent in the quarter and overhead expenses were up 3.4 percent, the lowest rate of increase in a year. Meanwhile, firms' productivity dropped by 2.5 percent as hiring rose.

Demand for legal services has been more or less unchanged since August 2011, according to the index.

"Such an extended period of essentially zero or negligible growth is worrisome as law firms both struggle to maintain their equilibrium in the shortterm, and try to plan for the road ahead," Peer Monitor said in a release.

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