The Prince William County Board of Supervisors voted yesterday to ask Virginia Gov. Mills E. Godwin for the power to implement mandatory restrictions on water use similar to those in effect in Alexandria and Fairfax County because of the declining water level in the Occoquan Reservoir.

If the governor approves and the water level in the Occoquan continues to drop, the supervisors will vote next Tuesday to enforce the mandatory restrictions, Board Chairman Alice Humphries said.

Meanwhile, police in Alexandria will start issuing summonses today to violators of the city's mandatory water conservation measures. If convicted, the violators face up to $500 fines.

Although restrictions on water use have been in effect in the city since Saturday, the City Council ordered police to issue only warnings during the first four days of the restrictions to allow residents time to become acquainted with the new rules.

A police spokesman reported yesterday that the department had issued only warnings, mostly for improper use of hoses. The spokesman said some of those warned protested that they were not aware of the restrictions.

The water level in the reservoir fell to another all-time low yesterday. It now is 101 feet above sea level, which means the reservoir contains a little less than 3 billion gallons of water, less than one-third of its capacity.

The water level has declined 4 inches each day for the last seven days, according to Fairfax County spokesman Edmund L. Castillo.

The Fairfax County Water Authority, which owns the reservoir, supplies water to about 600,000 people in Fairfax, Alexandria and Prince William.

Humphries said the supervisors decided to ask the governor for the power to implement mandatory restrictions after the Board was told yesterday that the reservoir's level is declining steadily.

Prince William officials had refused last week to impose mandatory restrictions, but urged its citizens to conserve water voluntarily.

In Alexandria, the restrictions prohibit the washing of automobiles and other vehicles except in wash facilities that use recycled water, or with a container whose capacity does not exceed three gallons.

The watering of lawns or shrubbery is also illegal except in the case of greenhouse or nursery stocks and lawns and sod less than five weeks old. Watering is allowed in all cases, however, if a container that holds no more than three gallons of water is used.

Swimming pools or wading pools requiring more than five gallons of water may not be filled except of insure that the pool's structure is not damaged.

The washing of streets or driveways and the operation of ornamental fountains is also banned. The fountain in front of city hall has been shut off for two weeks on the orders of City Manager Douglas Harman.

Restaurants in the city are forbidden from serving drinking water except when customers request it, and operation of air-conditioning units has been restricted to those with water-conserving equipment.

Fairfax's restrictions are similar to Alexandria's and Humphries said that if Prince William enacts mandatory restrictions, its regulations will follow the same pattern.

In Fairfax Cunty, police issued summons to four people last weekend who were washing their cars in violation of the county's water conservation restrictions. They face up to $500 fines.