Anne Arundel and Howard county voters, who have previously elected council members countywide, overwhelmingly opted yesterday for election systems that will require candidates to be nominated and elected by voters in their home districts.

In a separate race in Howard County, school board candidate Anne Dodd, the village manager for the Columbia subdivision of Kings Contrivance, defeated Allen F. Swanson, a speech pathologist in the Baltimore County school system, for a seat vacated by board member Stanley Stalett, who decided he would not seek a second six-year term. With all of the 53 precincts reporting, Dodd had 23,690 votes, 59 percent of the vote, to Swanson's 16,703, or 41 percent, according to unofficial returns of the 40,393 voters.

Final unofficial vote tallies in Anne Arundel County, which had two ballot questions dealing with district elections, showed 66,688, or 78 percent of the 85,318 voters, in favor of Question C, which mandated council members be nominated and elected from the district in which they live. Those opposed numbered 18,630, or 22 percent.

Under the current system, council members must be nominated from the district in which they live, but are elected countywide.

The passage of Question C effectively eliminated another proposal, Question B, which would have reestablished a system of countywide primaries and general elections. It was rejected by a vote of 50,656 to 27,736.

In Howard County, which had one question on the issue, 26,353 persons, or 58 percent of the 45,292 voters, were in favor of changing the election system and 18,939, or 42 percent, were against, with all of the precincts reporting.

District elections in both counties will go into effect in 1986.

David W. Kelley, an Annapolis banker who headed the petition drive for district elections in Anne Arundel, described the decision as a mandate by the people. "This is undoubtedly a vote for the people," Kelley said.

Councilwoman Maureen Lamb (D-Annapolis) said she was disappointed with the results, which she believed will hurt county decisions. "Ninety-five percent of our issues are countrywide issues. Why should I be elected by one district."

In Howard County, leaders of both sides of the issue said they were surprised by the election results.

"Obviously I'm very excited and very pleased," said D. Craig Horn, chairman of Howard Countians for Councilmanic Districts, a citizens' group that gathered petitions to place the question on the ballot.

L. Russell Gobbel, cochairman of the group that opposed the referendum, said he believed a large turnout of Republican voters and a strong showing by President Reagan in Howard County made the difference. "It looks basically like those who voted for Reagan also voted for districting," he said.

Theodore G. Bloom, the incumbent for the Court of Special Appeals for the Fifth Appellate Judicial Circuit that includes Anne Arundel and Howard counties, received the voters' approval yesterday. In Anne Arundel County, Bloom received 57,505 votes to continue in office with 9,990 opposed. In Howard County, he received 30,233 votes to continue with 4,646 opposed.

Contributing to this story were special correspondents Kaye Thompson and Keith F. Girard.