Democrat Patrick J. Holland and Republican Robert J. Sweeney jumped to early leads over their opponents yesterday in primaries for Alexandria city sheriff.

With about one-third of the precincts reporting, Holland was slightly ahead of his Democratic opponent, Theodore Dodd. Sweeney and his Republican opponent, Michael E. Norris, were locked in a tight race.

Turnout in Alexandria was extremely light. Officials said a slight rain may have contributed to the lack of voter interest.

Holland, 30, is a real estate manager with no law enforcement experience, but he was backed by many of the city's elected Democratic officials. Dodd, 41, is a former deputy sheriff.

Sweeney, 46, is an Alexandria businessman and has served as an unpaid volunteer deputy sheriff on an on-call basis since 1973. He was supported by Alexandria Mayor Frank E. Mann and an influential group of lawyers in the city. Norris, 28, is an Alexandria police sergeant an demphasized his law enforcement training during the campaigning.

Alexandria has about 44,000 registered voters.

The winners of yesterday's Democratic and Republican primaries, in addition to facing each other in the Nov. 8 general election, will be pitted against three independent candidates who have filed for sheriff.

The three independents are Walter T. McDonald, the owner of an Alexandria restaurant and a former District of Columbia policeman, and two city employees, Robert E. Evans and Robert D. O'Hern. Evans is Alexandria City Hall communications and records supervisor and a former Alexandria policeman. O'Hern is deputy clerk of the General District Court.

Interest in the sheriff's race was high this year because there is no incumbent seeking re-election. Raymond E. Fogle, the city's last elected sheriff, was forced to retire in March after a special investigator uncovered expense account padding among some members of the sheriff's staff.

Several of Fogle's employees were forced to repay more than $6,000 to the city and state. Fogle had been sheriff since 1964. Louise Armistead, a former deputy sheriff, was appointed acting sheriff but did not seek election to a full term.

In Alexandria, the sheriff is responsible for the jail, transporting prisoners, serving court papers and providing courtroom security. The department has a staff of about 60. When he retired, Fogle's salary was $23,800, all of it paid by the state. The sheriff's salary is determined by his experience and background, and can be supplemented by the city.

All four candidates running in yesterday's primaries promised to reform the department's procedure for filing expense accounts.