Republican Barbara Comstock narrowly won the 34th District in 2009. In 2013, she won again by just 422 votes. Now she is vacating the seat because she’s headed to Congress. (J. Lawler Duggan/For The Washington Post)

In a political district that analysts say is evenly split between Republican and Democratic voters, the race to succeed Barbara J. Comstock in Virginia’s House of Delegates is likely to be close.

That appears to have made Democrat Kathleen Murphy and Republican Craig Parisot wary of saying anything that could alienate voters in the Jan. 6 special election, which was scheduled after Comstock (R) won a seat in Congress.

In an interview, Murphy, 66, avoided sharing specific ideas for legislation she would introduce. Instead, she cited ongoing efforts in the House of Delegates that she would support, such as gun control and requiring colleges to report sexual assaults to police.

“We’re running on the issues, and we’re making sure we’re getting our message out to voters,” said Murphy, who narrowly lost to Comstock in November 2013. Because of her brother’s 1998 shooting death, gun control in particular is an issue she cares deeply about, Murphy said.

Parisot, 41, declined to be interviewed by The Washington Post.

The candidates have been canvassing for votes in a district that stretches from the Potomac River through McLean, Great Falls and portions of Loudoun County — a sprint through some of Virginia’s wealthiest neighborhoods.

Voters do not register by party in Virginia, but recent elections suggest that the 34th District has about equal numbers of Republicans and Democrats.

Comstock, who narrowly won the seat in 2009, beat Murphy in her bid for another term last year by 422 votes. In the 2012 presidential election, 50 percent of 34th District voters favored President Obama, and 49 percent went for Republican Mitt Romney, according to the University of Virginia’s Center for Politics.

“It’s a pretty 50-50 district,” said Geoffrey Skelley, associate editor at the center’s Sabato’s Crystal Ball.

That makes the January election a rare opportunity for Democrats to gain ground in a state General Assembly dominated by Republicans. But with historically low voter turnouts in special elections, Republicans may have the edge: They have shown greater willingness to show up at polls in years when there isn’t a presidential election.

“If Democrats have any hope of winning the House of Delegates, they have to win seats like this,” Skelley said.

The 34th District is home to lobbyists, federal contractors and others with deep ties to nearby Washington. It comes as no surprise, then, that both candidates also have strong connections to the federal government.

Murphy is a consultant who helps businesses and nonprofit groups navigate the federal legislative process. She is a member of the Fairfax County Human Services Council and has worked as a senior adviser for international trade issues for the Commerce Department.

Murphy was also once an aide to U.S. Rep. Charlie Wilson, the Texas Democrat whose role in a covert operation that aided the mujahideen during the Soviet war in Afghanistan was depicted in the 2007 movie “Charlie Wilson’s War.”

“What I have is 30 years’ experience handling legislative issues on all kinds of levels,” she said, mentioning her role in co-founding the Salute Our Services nonprofit for military families as one of her accomplishments.

Parisot, a former Air Force captain, heads a Washington-based consulting group that aims to help businesses operate more efficiently. He is also president of the Volunteer Fairfax business philanthropy group.

Parisot previously worked as chief strategy officer for a defense contracting firm that developed cloud-computing software to help intelligence operations in Afghanistan. In 2004, he ran for mayor in Cheverly, Md., receiving four votes out of 64 cast, according to town records.

On his Web site, Parisot promises to push for more funding for schools and transportation. Additionally, he vows to support fewer regulations and taxes for Virginia businesses.

“If there is one thing I want people to know about me, it’s that I’m not looking for purpose by running; I’m running with purpose,” Parisot said recently in a rare interview he granted to the Connection newspaper chain.

In response to interview requests from The Post, Parisot’s campaign initially asked for questions to be e-mailed in advance. But the campaign ultimately declined to make Parisot available for comment, citing his busy campaign schedule.

Some voters say they feel a sense of fatigue about the race, particularly so soon after the November elections.

A weary look flashed across Mary Ulmer’s face when she answered the door recently and greeted a cheerful Murphy.

“I’m tired,” Ulmer, 73, admitted with a smile after promising Murphy her vote. “I’m not looking forward to another election.”