Kyle Chrisley Allegedly Punched Cops, Threatened to Kill Police

Kyle Chrisley, the son of "Chrisley Knows Best" stars Todd and Julie Chrisley, punched three cops and threatened to kill the officers ... at least according to the police who arrested him in Tennessee.

TMZ obtained the affidavit from Kyle's Saturday arrest in Rutherford County, and cops say they got a call from Josh's wife, who told dispatchers he was making suicidal and homicidal threats.

Police say when they arrived, Kyle walked away from them and refused their commands ... and they say he eventually turned around and got aggressive and combative with them.

Things turned physical, police say, with Kyle punching three different officers in the face and head ... causing multiple injuries.

And, get this ... cops say Kyle told the officers he "would kill all of them."

Cops say Kyle's wife told them they were out to dinner earlier in the evening when Kyle suddenly picked up a fork, held it towards her, and threatened her ... and then on the drive home, he yelled at her and made her "fear that he would assault her."

Sounds like alcohol may have been a factor here ... cops say Kyle admitted to drinking approximately 64 ounces of beer at the restaurant ... and police say he appeared to be under the influence.

TMZ broke the story ... Kyle is facing charges of domestic assault, public intoxication, disorderly conduct, assaulting a law enforcement officer, resisting arrest, disorderly conduct, and retaliation for past actions.

We reached out to Kyle's attorney ... so far, no word back.