US actor Jonathan Joss has been shot dead in what his husband says was a homophobic hate crime, although police have said they have found no evidence of that.

Joss, 59, was known for voicing John Redcorn on long-running TV animation King of the Hill, and played Chief Ken Hotate in sitcom Parks and Recreation.

His husband Tristan Kern de Gonzales said a man "started yelling violent homophobic slurs" then opened fire when they were visiting their former home, which was destroyed in a fire in January.

Police in Texas said: "Despite online claims of this being a hate crime, currently the investigation has found no evidence to indicate that the Mr Joss's murder was related to his sexual orientation."

The shooting happened when the couple went back to the site of their old house, which "was burned down after over two years of threats from people in the area who repeatedly told us they would set it on fire", Gonzales wrote on Facebook.

"When we returned to the site to check our mail we discovered the skull of one of our dogs and its harness placed in clear view. This caused both of us severe emotional distress. We began yelling and crying in response to the pain of what we saw," he wrote.

"While we were doing this a man approached us. He started yelling violent homophobic slurs at us. He then raised a gun from his lap and fired.

"Jonathan and I had no weapons. We were not threatening anyone. We were grieving. We were standing side by side. When the man fired Jonathan pushed me out of the way. He saved my life."

Gonzales added that Joss "gave me more love in our time together than most people ever get", and that they were in the process of looking for a trailer after getting married on Valentine's Day.

"I was with him when he passed. I told him how much he was loved."

Officers found Joss lying near a road in San Antonio after being called to a report of a shooting, CBS reported.

A suspect, Sigfredo Alvarez Ceja, has been arrested on suspicion of murder.

San Antonio Police Department's statement added: "Investigators handle these allegations very seriously and have thoroughly reviewed all available information.

"Should any new evidence come to light, the suspect will be charged accordingly."

Parks and Recreation actor Nick Offerman paid tribute to Joss, telling People: "The cast has been texting together about it all day and we're just heartbroken.

"Jonathan was such a sweet guy and we loved having him as our Chief Ken Hotate. A terrible tragedy."

King of the Hill's creators Mike Judge, Greg Daniels and Saladin Patterson said in a statement: "Jonathan Joss brought King of the Hill's John Redcorn to life for over a dozen seasons, including in the upcoming revival.

"His voice will be missed at King of the Hill, and we extend our deepest condolences to Jonathan's friends and family."

Variety said Joss was most recently seen in public on Friday during a King of the Hill panel at the ATX Television Festival in Austin, Texas.

He was present in the audience, and had previously written on Facebook about his hurt at not being invited to be on the panel.

"This show was a part of my life for many years," he wrote in April.

"That character, that voice, that story... they were my home, my pride, my connection to something bigger than myself. To not be invited felt like being shut out of a place I helped build."

The show, set in Texas, is about the life of propane salesman Hank Hill and his family and friends. It was created in 1997 by Mike Judge and Greg Daniels and ran for more than 250 episodes.

It is now being revived, and the new season will be available on Hulu from 4 August.