DeMarcus Cousins just caught a huge break in his harassment case ... the NBA star's charges have been dropped, TMZ Sports has confirmed.
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.