DENVER—When Eric Church performed at Ball Arena recently for 16,000 fans, the first to arrive wasn’t a member of his Church Choir fan club—it was a pair of Covid-19-sniffing dogs named Alex and Timmy.

The country-music superstar has been touring this fall while Covid-19 cases remain high. Every show day, starting around 7 a.m., specially trained dogs screen band members, roadies and local workers. If they detect Covid, a test is required. It’s a way to boost safety while capping costs.

“It’s probably saved the tour,” says Todd Bunch, Mr. Church’s tour manager and certified Covid officer, who has lingering symptoms from his own bout with the illness months ago.