Jonathan Joss‘ husband Tristan Kern de Gonzales is convinced he was gunned down in cold blood by a neighbor due to homophobia — but cops are pumping the brakes, saying they’re not calling it a hate crime just yet.

The actor — best known as the voice of John Redcorn on “King of the Hill” — was shot dead on his own property Sunday evening — and cops are saying that right now there’s not enough proof to back up Tristan’s claim it was a hate-fueled attack.

San Antonio Police posted an update on X Monday, writing, “Despite online claims of this being a hate crime, currently the investigation has found no evidence to indicate that Mr. Joss’s murder was related to his sexual orientation.”

That’s a direct hit against Tristan’s viral post — where he flat-out accused their neighbor of being motivated by hate … claiming he’d made threats before and even hurled a homophobic slur the same day Joss was killed.

Cops and eyewitnesses told TMZ the two neighbors got into a heated altercation — before the neighbor allegedly shot Joss and drove off.

Sigfredo Alvarez Ceja was arrested on suspicion of murder and was held in custody on a $200K bond.