In a blow to local governments that rely heavily on property-tax revenue to fund schools and other services, seven of the Bay Area's nine counties saw their assessed property values fall 1% to 4% as of Jan. 1 from a year earlier, according to a report due Thursday from Santa Clara County Assessor Larry Stone. In Santa Clara, total assessed property values—including residential and commercial property and business equipment—fell 2.3% to $311 billion. That marked the first annual decline since the Great Depression, excluding 1978 when Proposition 13 rolled back property-value assessments across California, Mr. Stone says. Only San Francisco posted a notable increase—of 4.25%—in assessed property values, partly because it saw less overbuilding during the boom and demand for property held up better during the downturn, says San Francisco County Assessor-Recorder Phil Ting. Napa County was the only other gainer, with a 0.2% increase.