The Washington Bullets have signed oft-injured small forward Bernard King of the New York Knicks to an offer sheet, it was learned last night.

King, a free agent who earned $874,000 last season from the Knicks, signed what is believed to be a multiyear offer sheet in the neighborhood of $1 million a year from the Bullets. The Knicks have 15 days to match the offer, but King's attorney, Bob Woolf, said it was unlikely New York will try to retain King.

"There have been several clubs interested in Bernard, and the Knicks haven't shown much interest in signing him," Woolf said. "I'm confident he will be with Washington this season."

King damaged ligaments and cartilage in his right knee in March 1985 and, since surgery, has played sparingly.

"There is a gamble here {because of King's injury history}, but we feel that, if everything goes okay, he will help us a lot," said Bullets General Manager Bob Ferry. "He's really excited about playing here. With his addition, he thinks we have a good chance of winning here."

King was in Washington on Thursday, at which time he was examined by doctors and came out with a clean bill of health, Ferry said. King also was in Boston this week, passing a physical given by Boston Celtics physicians.

King, 30, led the NBA in scoring in the 1984-85 season at 32.9 points a game, but a knee injury that season limited him to 55 games, then he missed the entire 1985-86 season and played only the last six games of last season. A 6-foot-7, 205-pounder, he has a career average of 23.7 points a game and a career shooting percentage of 53.8.

He opened his NBA career with the New Jersey Nets, playing the 1977-78 and '78-79 seasons under current Bullets Coach Kevin Loughery. That tie with Loughery apparently influenced King's decision to sign with the Bullets.

"Bernard wanted to be with Washington," Woolf said. "He played with Kevin before, he liked the situation in Washington and he liked the players."

If King becomes a Bullet, it would crowd the small forward spot, where Jay Vincent was expected to get a lot of playing time. His acquisition is designed to plug a big Bullets weakness -- scoring punch. "That's an area we have needed help in," Ferry said.

The Knicks, who signed forward Sidney Green of the Detroit Pistons to an offer sheet last week, were known to be disgruntled with King, particularly because of his rehabilitation process in which he stayed away from the club and its practices.