Washington-based law firms struggled to grow their business during the first half of the year, lagging law firms nationwide in three key financial measures, according to a new survey of U.S. law firms.

Revenue, demand and productivity — the number of hours that lawyers billed their clients — all fell more rapidly among D.C.-based law firms than they did at law firms nationwide in the first six months of 2013 compared with the same period last year, according to data compiled by Citi Private Bank Law Firm Group. The group surveyed 172 law firms nationwide, including 12 Washington-headquartered firms.

The data represents a limited snapshot of the local legal market, surveying only law firms headquartered in the District — and leaving out the many law firms that are headquartered elsewhere but have a significant presence in this region. The data, however, does contain a representative slice of the region’s legal industry by including large, mid-size and smaller firms. And the findings are significant because they go against the long-held conventional wisdom that Washington firms, with their proximity to the constant churn of government-related work, have weathered the recession better than those in other regions where legal work is more susceptible to market downturns.

Here’s how D.C. firms fared:

Revenue at D.C.-based firms dropped 2.4 percent, while revenue at firms nationwide grew 0.5 percent.

Demand for legal services at D.C. firms fell 2.5 percent, while demand at firms nationwide dipped 1.3 percent.

Productivity at D.C. firms declined 4 percent, while productivity at firms nationwide fell 1.7 percent

Meanwhile, expenses continued to climb at D.C.-based firms, though they did so at a slightly slower rate than at firms nationwide. D.C. law firms saw expenses rise 2.2 percent, compared to 2.4 percent nationwide.

“When you’ve got modest revenue growth and expenses growing at a higher rate, it puts pressure on your profit margin,” said Gretta Rusanow, senior client adviser at Citi’s Law Firm Group. “If demand continues to decline, it’s going to be difficult for firms, whether they’re in the D.C. market or broadly speaking, to generate enough revenue to ease the pressure on margins.”

The one area where Washington-based firms outpaced their counterparts was size: Local firms grew 1.6 percent in attorney head count, while firms nationwide inched up 0.4 percent.

However, that could be why attorneys in D.C. are logging fewer hours of billable work, Rusanow said.

“If you’ve got less demand for legal services, but more lawyers to keep busy, it means there are fewer hours to share across that larger group of lawyers,” she said.

Washington-based firms also fell behind in “inventory” — the number of billable hours that firms have built up, but have yet to be paid for (in other words, future collections). While law firms nationwide saw inventory grow 2.7 percent, D.C.-based firms saw inventory slip 0.8 percent.

“When we see a buildup in inventory, that signals it’s setting the industry up for a stronger quarter because it’s waiting to be collected on,” Rusanow said. “D.C. was not in a good position ... it suggests a challenging third quarter for D.C.-headquartered firms.”