NBA Star Nick Young -- Cops say Rape Accuser's Story's 'Crazy', 'Unbelievable'

NBA star Nick Young is being sued by a woman who claims he raped her, but law enforcement sources tell TMZ ... when she went to cops with the allegations, they dismissed them as bogus.

As we previously reported, the woman claims Nick -- a member of the Philadelphia 76ers -- slipped a date rape drug into her drink at a Hollywood bar in 2011, took her to his home and raped her vaginally and anally.

She's filed a civil lawsuit, but now we're learning shortly after the alleged incident, she went to LAPD cops who dismissed her claim because her story didn't make sense. What's more ... law enforcement says at the time she went to cops, she was already talking about a lawsuit, and that made them even more suspicious.