July 27 (Reuters) - Law firms saw an increased demand in labor and employment work during the second quarter of 2012, one of the only practice areas that has been consistently strong amid a tough market, according to data complied by Peer Monitor.

The uptick in labor and employment, which increased in demand by 4.2 percent, came at a time when legal services as a whole saw a 0.2 percent drop in demand, according to the Hildebrandt Institute's Peer Monitor Index issued Friday.

The index, which measures law firm profitability on a quarter-by-quarter basis, is determined by a number of variables, including billing rates, expenses, productivity and demand.

The Hildebrandt Institute is a division of Thomson Reuters.

The report found that litigation work was flat in the second quarter, while demand for corporate work fell 2.1 percent. Real estate and bankruptcy work also took a hit, with demand dropping by 3 percent.

In terms of geography, Los Angeles proved to be the hottest market, showing an uptick of 5 percent in legal work, while Silicon Valley trailed with an increase of 2 percent in demand. The demand for work in New York and Chicago were both down by 1 percent and Washington declined 2 percent.

As a whole, the report said that law firms' productivity fell 2.5 percent in the second quarter and that there was not sufficient work for lawyers at firms. The number of attorneys on staff increased 2.3 percent, the report said.

Mark Medice, program director of Peer Monitor, said he was concerned that law firms are not doing enough to manage their expenses and cited a rise in direct and overhead expenses in the second quarter.

"I'd say for 2012 it's going to remain a challenging year," said Medice. "Law firms have seen expenses growing but top line revenue remained fairly flat."

(Reporting By Casey Sullivan)

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