Only four cities or counties in the Washington region have fully rebuilt their property tax bases since the 2008 recession, a study from George Mason University’s Center for Regional Analysis says, raising questions about the wisdom of tying local government operating budgets to the real estate market.

The anemic tax base poses a challenge to city and county governments, even as Maryland and Virginia are seeing statewide budget shortfalls linked to reduced government spending in the region.

Property values have stagnated in most suburbs since 2005, said David Versel, the senior research associate who wrote the report, although they have grown in the District, Alexandria, Va., and Arlington and Loudoun counties in Virginia.

“People might be surprised to learn how much Montgomery County and Fairfax County are struggling,” Versel said. “They’re thought of as powerhouse jurisdictions. But they’re clearly in a transition from affluent suburbs to whatever they’re going to become.”

Nine of the 13 biggest municipalities in the Washington area draw at least half of their general, or operating fund, revenue from property taxes. In Fairfax, Loudoun and Prince William counties in Virginia, property tax revenue accounts for more than 60 percent of operating funds.

The District and the Maryland suburbs rely on local income taxes in addition to property taxes, but Virginia counties and municipalities cannot tax income.

Across the region, strong growth in property values between 2005 and 2009 drove tax assessments up 57.7 percent. But the next two fiscal years saw assessments drop 12.3 percent, before beginning a slow, and so far uneven, recovery.

In all parts of the region, recent growth in housing has been concentrated along Metro lines and close-in locations, Versel wrote. “This trend has contributed to the assessment increases in the District, Arlington and Alexandria, and it has helped Fairfax, Montgomery and Prince George’s survive the assessment declines for their other property types.”

Assessments in Fairfax, Virginia’s largest county, dropped 18 percent between 2009 and 2011, and climbed only 9 percent in the subsequent three years.

Montgomery’s property tax assessments stalled earlier and dropped further than other Maryland suburbs during the recession, but its residential assessments have since stabilized and the commercial market has improved as well, Versel’s report said.

In general, however, “the office market in the region is in terrible shape,” Versel said in an interview. With high commercial vacancy rates in many jurisdictions, he said, most local governments cannot turn to commercial property taxes to make up for the lackluster residential market.

Local governments must therefore raise taxes on homeowners, cut spending or both, he warned.

Although the report did not include other revenue-generating proposals, it concluded that “new approaches . . . may be needed to help city and county governments avoid experiencing continued fiscal challenges in the next few years.”