This girl is just dumb dumb dumb! TMZ REPORTS  Call her crazy … but Karrueche Tran and Chris Brown are full-on LIVING TOGETHER … TMZ has learned. Sources close to the couple tell TMZ … they hooked up days before his 24th birthday earlier this month and she’s been staying at Chris’ Hollywood Hills home ever since. Though she’s keeping her own apartment — smart — she’s already moved most of her clothes and other personal belongings to his pad. And it’s not like they’ve been secretive … they’ve been spotted everywhere lately, hitting up the Billboard Awards afterparty and even rear-ending a Mercedes together. Karrueche’s one persistent scorned lover — when Chris first dumped…