WASHINGTON — Virgil Goode, the presidential nominee for the conservative Constitution Party, qualified Tuesday for Virginia’s ballot in November, complicating Mitt Romney’s chances of winning the key swing state. Polls show a tightly contested race between Mr. Romney and President Obama.

The Virginia State Board of Elections announced Tuesday that Mr. Goode’s name would appear third on the ballot, following the Republican and Democratic presidential nominees. At the same time, the board asked Kenneth T. Cuccinelli II, the state’s Republican attorney general, to investigate Republican allegations that Mr. Goode’s party used fraudulent signatures to qualify for the election.

“Candidate Romney, before he continues campaigning, should read the First Amendment about free speech and the right to petition,” Mr. Goode said Tuesday. “They’re afraid true conservatives will vote for me.”

The Republican Party of Virginia vowed to continue its fight to knock Mr. Goode’s name off the ballot before voters go to the polls. Pat Mullins, the party chairman in Virginia, accused Mr. Goode of “systemic problems” in his signature petitions worthy of a criminal investigation.