The 70-year-old said he started feeling ill Monday. He contacted Memorial Hermann about his symptoms, and he got tested as soon as possible.
League City administrators said they learned Tuesday that Hallisey tested positive, and they began evaluating where Hallisey had been and who he had been in contact with.
Hallisey attended the council meeting Nov. 10, the Veteran's Day ceremony the following day and the College of Mainland groundbreaking event the next.
There were state and local representatives at the events, including U.S. Representative Randy Weber and Texas State Sen. Larry Taylor.
Hallisey is at home with a sore throat, according to his team. He was treated for a heart attack in 2017, shortly following Hurricane Harvey, which resulted in the amputation of his left leg.
All council members have been notified and been tested.