PETALUMA—Sonoma County is best known for picturesque vineyards and rolling hills. But some residents are up in arms about a less attractive distinction: the 2,718 miles of roads in the county's rural areas that are in worse shape than nearly anywhere else in the Bay Area.

Two-lane Lichau Road, for example, which winds up a hill outside the small town of Rohnert Park, has fallen into disrepair. It is crumbling at the edges and covered with different shades of gray from patches...