Alexandria Republicans go to the polls today to decide whether they want Sheriff Michael E. Norris to remain in office.

Norris, 37, who has held the $58,000-a-year position since 1977, is being challenged by Edward L. Clark, 65, a retired railroad police agent.

Polls in Alexandria will open at 6 a.m. and close at 7 p.m.

The primary is one of two in Northern Virginia. Republicans in the Annandale area of Fairfax County will pick either Robert E. Murphy or Richard N. Vannoy to face state Del. Vivian E. Watts in the November elections.

The winner in the sheriff's primary will face Jim Dunning, a federal probation administrator who is running as an independent in the November elections.

Dunning, who is barred by federal law from running as a partisan candidate, last week won the endorsement of the city's Democratic Party.

"I think Mike is a really good sheriff," said Clark, who is making his first bid for public office. "He has made major improvements but I think there are a lot of questions about him in the city."

Clark, who retired in 1981 after 35 years with the Richmond, Fredericksburg & Potomac Railroad Co., declines to say what the problems are and refers questioners to his supporters, who raise the issue of Norris' life style.

They note that the two-term sheriff said in a Washington Post interview last year that he had a number of gay friends and that he had socialized with them.

"Mike is too controversial," said Robert W. McCaslin, a member of Republican City Committee and one of Clark's supporters. "He has run the office well but his life style is offensive to me. I don't think people will support him."

Norris has said that his comments were taken out of context and that his critics fail to mention what he has done to improve administration of the city jail.

"I have changed this jail completely around," said Norris. "I set a course and a direction for leadership. This office is a truly professional working environment. I have been labeled as an expert in corrections and court security."

His work with the jail wins the strong praise of Mayor-elect James Moran, a Democrat. " . . . He is a professional who has done truly impressive things in the jail," said Moran.

Norris has a staff of 102, and his office oversees security at the city courthouse and serves court papers as well as running the jail.

About 1,500 people are expected to turn out for the primary, according to Republican Party Chairwoman Jane Ring. Because voters in Virginia do not register by party, there is no restriction on who may vote in either the Alexandria or Annandale primary.