OROVILLE, CALIF. -- Rural Butte County's Board of Supervisors voted yesterday to file for bankruptcy unless the state helps cover its $14.1 million budget deficit. It would be the first U.S. county to take such action.

Supervisors of the largely agricultural county about 200 miles northeast of San Francisco authorized county attorneys to declare Chapter 9 bankruptcy unless the state legislature votes to grant funding for its fiscal year 1990-91 budget.

Services in the county have steadily deteriorated, with sheriff's deputies patrolling in rented cars and a county officials calling health conditions worse than those in developing countries.

California lawmakers were meeting in their final session of the year last night. If the legislature offers the county funding, supervisors said they may meet again before Sept. 7, when attorneys are scheduled to file for bankruptcy protection, to evaluate the offer.

Larry Naake, director of the County Supervisors Association of California, said other rural counties in the state are also in dire need of state funding.

"It is a growing problem and other counties are close behind unless there is some very basic structure reform in state and county finances," Naake said.

Supervisors blame low property-tax revenues caused by the passage of Proposition 13, the 1978 California law that limited property taxes and sparked a tax revolution across the nation. The county's problems also stem from a slow-growing property tax base, low non-property tax revenue, a loss of its tax base due to annexations, redevelopment projects and the incorporation of a community called Paradise.

The county's revenue increased 26 percent in the last decade compared to an inflation rate of 48 percent. County employees have not received a raise in four years. In 1980, the county of 185,000 had 59 sheriff's deputies; it now has 38.