Jackson Family Fight Case -- CLOSED

No one in Michael Jackson's family will be prosecuted over the fight last July at Katherine's home ... TMZ has learned.

As you recall, Paris and Prince got into it with Janet ... the video shows Janet confronting Paris and then apparently trying to get at her cell phone.

Paris then charged past Janet, who is then restrained by Randy. There was subsequently a physical confrontation ... we're told between Randy and Jermaine on one side, and Trent on the other.

Law enforcement sources tell TMZ ... the case is now closed because no one from the Jackson family would speak to cops. In fact, we're told none of them even returned various calls from detectives.