The Montgomery County Council asked the County Transportation Department yesterday to analyze the causes of every accident that has occurred this year at Chevy Chase Circle and called on the State Highway Administration to "take immediately action" to improve safety at the site "even if it means cutting down the trees.

The Council's action was prompted by an accident last week in which three persons were seriously injured when their car crashed into one of the trees on the Maryland side of the circle and burst into flames. There have been 59 accidents at the circle this year, according to traffic officials, making it the most dangerous of the District of Columbia's many traffic circles.

In July, 1976, four Metro garage mechanics were killed when their car slammed into the same oak tree that was struck last week. Two weeks later, a 16-year-old girl was critically injured in a crash involving the same oak.

A number of safety improvements have been made at the circle on the District of Columbia-Montgomery County line since the 1976 accidents, according to traffic officials. Among them are the addition of white lane markers, flashing arrows, and large yield and warning signs.

It is unclear what additional safety measures might be agreed on short of cutting down the circle's dozen tall oak and maple trees, most of them over 75 years old. But the possibility of cutting down the trees did not please some residents who live near the circle and who were surveyed informally yesterday.

"I have all the sympathy in the world for people who are hurt in accidents, but I believe those people who ran into the trees would have had an accident anyway," said Eleanor Leavitt, who lives on Montgomery Street about three blocks from the circle.

"My feeling about the tree accidents is that they wouldn't have happened unless the people involved in them hadn't been going twice as fast as they should, or hadn't been drinking or fallen asleep at the wheel," she said.

"I can't see why the trees are at fault," said another resident on Montgomery Street, who asked not to be named."If a person is going to be issued a driver's license, then that person has a certain responsibility to drive carefully."

Councilwoman Esther Gellman said she proposed making a study of the causes of accidents to see if there is a "common factor" involved in most of them. "Then we can work on the solutions," she said.

Council President John Menke, who proposed writing a letter about conditions at the circle to the state, said he realizes "citizens will probably object to cutting down the trees, so (the state will) have to look at other alternatives."