Jonathan Joss, the actor best known for his voice work on the animated television show “King of the Hill,” was shot and killed by a neighbor on Sunday night during a dispute in San Antonio, the authorities said.

Mr. Joss, who was 59, voiced John Redcorn on “King of the Hill” and also appeared in “Parks and Recreation,” “Ray Donovan” and “Tulsa King.”

The neighbor, who was identified by investigators as Sigfredo Ceja Alvarez, 56, was taken into custody shortly after the altercation and charged with murder, the San Antonio Police Department said on Monday.

The police did not say what had led to the dispute, which happened around 7 p.m. on the south side of San Antonio.But in a post on Mr. Joss’s Facebook page on Monday, his husband, Tristan Kern de Gonzales, described the shooting as a hate crime and said that the two of them had been repeatedly harassed because they were gay. He wrote that they had returned to a property where Mr. Joss’s home had burned down earlier this year when the shooting occurred.

“He started yelling violent homophobic slurs at us,” he wrote in a statement. “He then raised a gun from his lap and fired.”

Mr. Kern de Gonzales said that he and Mr. Joss had reported the harassment several times in the past to the authorities, but that it had continued.