Voters in Loudoun and Fairfax counties appeared confused by the eligibility requirements of the special election taking place Tuesday to fill the 33rd Senate District seat vacated by Attorney General Mark R. Herring, according to election officials.

The 39 Loudoun County polling sites in the district, which also includes parts of Fairfax, reported waves of voters Tuesday morning who were not eligible to vote in the election because they lived outside the district lines, according to Loudoun Registrar Judy Brown.

Part of the confusion, Brown said, was the fact that former state delegate Joe T. May is running in the election. May, a longtime Republican legislator who is running as an independent, represented Virginia’s 33rd House District for decades — confusing Loudoun voters who had previously supported him in his former district, Brown said.

“There’s confusion in the western part of the county because when people see or hear [May’s] name, they believe they should be voting,” Brown said. “Those people out west are showing up at voting places along with everyone else. ... there are voters in Loudoun coming out to vote no matter where they live.”

Brown said the registrar’s office had a “tremendous” number of calls Tuesday about the misunderstanding. Voters residing outside the 33rd district are not listed in the poll books because they are ineligible to vote, Brown said, but election officials at polling sites have been told to call the registrar’s office to confirm a voter’s eligibility before turning them away.

“People aren’t really paying attention, and I’m not sure what we could have done better or different to make people understand,” she said. “It’s made for a rather interesting day.”

Some Fairfax County voters also seemed uncertain about whether they were eligible to vote, according to Fairfax Registrar Cameron Quinn.

“Not everyone bothers to double-check that they are appropriately in the district before they show up, and there’s only so much that we can do,” she said.

Ten Fairfax County precincts fall within the 33rd Senate district, Quinn said, and of those, the Herndon Community Center in particular had turned away numerous county residents who were not eligible to vote in the special election.

“The good news is that while we’ve gotten a number of calls, most of them were before people got in their cars and left,” Quinn said.

Loudoun voters, meanwhile, appeared nothing if not determined: “There are some people who, if their polling place isn’t open, are driving until they find one that is and then they go inside,” Brown said.

The situation has created one more problem for election officials who are already faced with a winter storm that had closed county schools and the federal government, with the heaviest snowfall forecast for later in the day.

“It’s been a major issue,” Brown said, “and we haven’t even really gotten to the snow yet.”

(Voters can find a list of open voting precincts here.)