Republican candidate Kenny Blackwell said he is complying with the law and divides his time between the two properties.
The board said the discovery "does not necessarily indicate that illegal votes were cast in their names."
He also emphasized the importance of voter engagement.
Tuesday's order is expected to prompt legal challenges, as the president continues to try to interfere with state-run elections.
At an early voting site in Apex, a voter faced an issue when showing her ID.
The mailing, sent by the North Carolina State Board of Elections, is part of a statewide effort to ensure voter records match current databases and remain accurate.