After the police leave, Spade tries to get Brigid to explain exactly had happened between her and Cairo, but he can't tell whether she's still lying.
When asked about the black bird, Brigid says that it is a hawk or falcon, about one foot high, and that Floyd and Cairo had promised her $750 for helping them get it from a Russian named Kemidov.
After she had helped them find the bird, she discovered that Cairo intended to take the bird for himself, so she and Floyd decided to beat him to the punch. But when it came time for her share, Floyd refused to give it to her, and that's why she came to Spade for help.
Spade doesn't believe a word of Brigid's story, and tells her so. She doesn't deny it, but she also refuses to tell the truth.
That's when Spade kisses her (in the movie version, this would be the moment when the screen slowly fades to black).