“I was grateful for the opportunity to present the facts and I look forward to a quick resolution,” McKay said Tuesday in a statement.

Last week, Grayson P. Hanes, McKay’s lawyer, said that the potential violation would be a misdemeanor if the investigators conclude that the supervisor should have disclosed as a gift the difference between the $850,000 he and his wife paid for the house and its actual market value at the time. Hanes said McKay paid a fair price for the five-bedroom home.

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Neither the Virginia State Police nor the state attorney general’s office would confirm or deny that they are investigating the home sale. WAMU radio reported that the agencies were conducting a criminal probe.

That report, citing multiple anonymous sources, said Attorney General Mark R. Herring signed off on the inquiry in early August and that it is in its preliminary stages, with no charges filed.

The claims stem from an ethics complaint filed in May by developer Tim Chapman, one of three Democrats who lost to McKay in the June primary election for board chairman of Virginia’s largest jurisdiction.

In the complaint, Chapman alleged that McKay helped engineer the 2016 rezoning of a portion of the Kingstowne Towne Center inside Lee District — which he represents — as part of a deal on his home purchase nearly a year later.

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McKay and his wife bought their five-bedroom home in the Alexandria section of Fairfax for $850,000, which an investigation commissioned by Chapman claimed was less than comparably sized homes in that area. The sale price was slightly more than its assessed value.

The Chapman investigation, initially circulated in an anonymous memo, used public documents to suggest the purchase coincided with the June 2016 rezoning that allowed residential development on a five-acre portion of the massive Kingstowne site, which the county board approved unanimously.

The memo noted that, around the same time, developer Michael A. McGhan — a friend of McKay’s — was in the process of buying land that eventually became the site of McKay’s home from Kingstowne developer Warren Halle. Halle’s businesses have donated a total of $50,000 to McKay’s bid for chairman.

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If McKay had a business relationship with Halle during the time the rezoning was being considered, under state law he would have had to disclose it as a conflict of interest. Halle’s company owned the parcel that was rezoned.

Former county board chairman John F. “Jack” Herrity was convicted of a misdemeanor in 1986 for failing to disclose a relationship with a builder.

McKay said there was no such relationship. But he has acknowledged that McGhan sold the house he built on the land directly to him, without marketing it to other prospective buyers.

Hanes, a veteran land-use and real estate lawyer in Fairfax, investigated Chapman’s claims and called them “a witch hunt,” noting that the similarly sized homes used to suggest that ­McKay got a deal on his house were in more expensive neighborhoods.

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Still, even a suggestion of criminal wrongdoing could hurt McKay politically as he heads into the November election against Republican Joseph Galdo to replace Board Chairman Sharon Bulova (D-At Large), who is retiring after 30 years on the county board.

On Thursday, Bulova, a staunch ally of McKay’s who has groomed him for her seat, called the allegations “politically motivated.”

“Jeff is an honest, ethical colleague,” she said. “I would be surprised if these allegations are true.”

Galdo, whose chances of winning in the solidly blue county have been slim, pounced on the suggestion that McKay benefited financially from his friendship with a developer.

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