Gary Mankulish of Prince Georges Country Club, was the greyhound who finally caught the rabbit yesterday. He won the elusive District Golf Championship at Indian Spring, defeating Bethesda's Dave King, 6 and 5, in a 36-hole match.

Mankulish, who earlier this year won the Maryland State Amateur title, was runner-up in the District tournament in 1974 and 1975. King, 36, a statistician with the Public Health Service, is a two-time former Maryland State Amateur champion. He won those titles in 1969 and 1971 but never had been to the final of the District tournament before.

Mankulish, 24, is duplicating the best year in his career, 1975, when he was voted the No. 1 amateur in this area after winning the Middle Atlantic and Maryland state titles and finishing runner-up to Marty West in the District championship.

Mankulish, who works for an insurance frim, intends to paly in the prestigous Porter Cup Tournament and the Eastern Amateur. There have been persistent rumors he will try for his pro tour playing card in the fall.

Mankulish was 2-up after the morning round, when he won six holes and King four. King is one of the area's better scramblers and also one of the finest amateurs at the short game. He had a 76 in the morning, including a double bogey. Mankulish had a three-over-par 73. In the afternoon, Mankulish was even par through 13 holes and King four over. Mankulish hit eight greens.

The two golfers halved the first hole in the afternoon and Mankulish extended his lead to 3-up on the second hole, a par-three, when King pulled his shot over the green. It was symptomatic of King's tee shots all day. He penalized himself constantly by missing the fairway and was playing catch-up all day.

King won the third hole with a par, but Mankulish won the short fourth when te King again strayed on his tee shot. Mankulish birdied the fifth from seven feet to go 4 up and won the seventh with a par after a spectacular second shot. He was stymied by a small bush after his drive, but put a three-wood shot onto the green from 230 yards out.

Mankulish went 6 up on the eighth when he put his chip shot inches from ninth when Mankulish three-putted.

Mankulish came back to win the 10th when King put his drive in the water and bogeyed. King won the short 11th when Mankulish shipped poorly and took a bogey. The 12th was halved and then Mankulish won the match on the 13th when he roled in a 25-footer for a birdie 3.