We broke the story ... the Lakers center's ex-girlfriend, Cristy West, told police she recorded a phone call with Cousins in which he threatened to "put a bullet in your f**king head" if she wouldn't let their 7-year-old child attend his wedding.

Cousins was facing a domestic violence charge -- 3rd-degree misdemeanor for harassing communications -- which carries a maximum sentence of 1 year behind bars.

Cousins was slated to have his arraignment Friday -- but the case was dropped and won't be moving forward.

One source close to DeMarcus tells us, "It was a just and fair outcome."

Unclear exactly why the case was dropped but it's not unheard of for prosecutors to bail on a case like this if the victim stops cooperating with authorities.

Despite the court situation, the NBA is still investigating on their own and could mete out punishment if they deem necessary.