District of Columbia residents covered by State Farm Mutual Automobile Insurance Co. will pay higher insurance rates beginning July 1, and D.C. drivers covered by Government Employees Insurance Co., the biggest Washington-based auto insurer, began paying 8.5 percent more May 31.

State Farm's overall rates for the District will rise 11.4 percent, largely because of an increase in the number and cost of auto property damage claims filed against the Illinois-based insurer, company officials said yesterday.

State Farm's rates for Northern Virginia and the Maryland suburbs will remain the same for the foreseeable future, the company's officials said.

Geico will raise its rates for Northern Virginia and suburban Maryland drivers on Aug. 1. The overall cost of Geico's Virginia premiums will go up 8 percent compared with a 9.8 percent increase in Maryland. The two companies are among the largest in the District in terms of number of auto insurance policies.

The rate increases in the District have nothing to do with the city's no-fault insurance program that took effect on Oct. 1, 1983, State Farm and Geico officials said. Under no-fault, people injured in a traffic mishap are reimbursed for medical expenses by their own insurance companies regardless of who caused the accident.

"State Farm's no-fault claims in the District are rather low when compared with our no-fault experience in other states," State Farm spokesman Robert Sasser said.

"It will take us another six or nine months . . . to determine what, if any, effect no-fault has had on our claim activity," said Donn Knight, Geico's regional vice president.

A rapid increase in new-car purchases -- including many cars loaded with high-cost options -- and an increase in the number of miles all cars are driven each year are the principal contributing factors to the rate hikes, Knight said.

"In the last two years, people started buying new cars; and because of lower gasoline prices, people in the area simply are driving more, and running into each other more often," Knight said.

Geico's rate activity -- increases and decreases -- over the last five years works out to an annual raise of about 3.5 percent. That matches the current standing of the consumer price index, a measurement of price changes in selected goods and services sold in the United States.

State Farm's last general rate increase in the District, a 9.4 percent hike, came in October 1982. That means State Farm's new 11.4 general raise amounts to annual increases of 3.8 percent over the last three years.

Geico's Knight declined to say what the new increases will mean for the company's "typical insured driver" in terms of actual dollars and cents. "That's almost impossible to do," Knight said. "It depends on the age of the driver, the age and cost of the car" and a host of other factors, he said.

But State Farm's Sasser said his company's "typical insured driver" in the District can be described as an adult owner of a 1985 Chevrolet Impala, a standard-size, four-door sedan that, as of Jan. 2, 1985, carried a manufacturers's suggested base retail price of $9,709.

State Farm's "typical" client in the District currently pays an overall premium of $294.36 every six months. Under the new rates, that client will pay $309.32 biannually. "The rate change for individual customers will vary, depending on the coverages they carry, the kind of car insured, who drives it, and how much it is driven," State Farm officials said in a company statement.

Since 1983, State Farm's property damage liability claims in the District -- those made against the company's clients -- rose from 50 per 1,000 insured cars to 52.4 per 1,000 insured cars, Sasser said. Collision claims -- those filed by the company's clients -- rose from 120.9 per 1,000 insured cars to 124.8 per 1,000, he said.

Said Geico's Knight: "We had to respond to the increased accident frequency and rising costs. But the consumers can do something to help us and themselves. . . . If people would cut out a lot of drinking and driving, and if they would use their seat belts, we could save them a lot of money. Really."