The Supreme Court yesterday rejected without comment an appeal of a $4.35 million judgment against Arlington County for injuries caused a man who lost both legs at the climax of a high-speed police chase into the District.

The judgment is the largest award in a "hot pursuit" case in the country, the man's lawyer said.

The county had argued that it should not have to pay Alvin Biscoe, who was struck by a car driven by bank robbery suspects an Arlington officer had chased across the Roosevelt Bridge.

The fleeing car, traveling at about 80 mph, according to testimony in a 1983 trial in U.S. District Court in Washington, collided with another car and then pinned Biscoe against a lamppost at 19th and E streets NW as he was taking a lunch-hour walk from his office on Sept. 27, 1979.

Biscoe, 51, an official with the National Science Foundation, looked solemn as he rolled his wheelchair into a press conference yesterday and said he hoped the judgment would "send a message" to police around the country.

"Police departments need to be more mindful of protecting the public first, and catching bank robbers second," he said. "I wonder if police departments have their heads on straight if they think it's more important to play cops and robbers than to protect the public."

Arlington officials said yesterday they planned to pay the judgment, although many expressed disappointment the court refused to hear the appeal..

If the accident had occurred in Virginia, the county could not have been sued, because Virginia jurisdictions operate under a doctrine of sovereign immunity, meaning they are not liable for injuries that result from an employes' job performance.

During the 15-day trial in district court, Judge Harold H. Greene ruled that sovereign immunity did not apply in the Biscoe case because the District of Columbia does not recognize that principle.

The jury's decision, a judgment against the fleeing suspect, the police officer and the county, awarded $4 million to Biscoe and $1 million, later reduced to $350,000, to his wife, Eleanor. Interest has brought the sum to more than $5 million.

Since 1982, Milliken said, the county has set aside money from its general tax funds, an amount now "somewhere around $4.3 or $4.5 million" without interest, in anticipation of the judgment. He said the payment "will not have any current impact" on county tax rates.

After Biscoe's press conference, his attorney, Joseph H. Koonz, came close to tears when he recalled a moment at the end of the trial, when the bank robber whose car hit Biscoe came forward, placed his hand on Biscoe's and said, " 'I'm really sorry. I didn't mean to do this to you.' "