Native Son to p.209

Quote
"The big white cat bounded down the steps and leaped woth one movemment upon Bigger's shoulder and sat perched there. Bigger was still, feeling that the cath had given him away, had pointed him out as the murderer of Mary" (202).

Significance
I chose this because I think this cat might be Bigger's down fall. The cat was the only one to see him actually kill Mary. While the cat cannot talk, seeing how Bigger reacted to the cat just sitting on him, I think that just the fear of the cat might betray him. How exactly, I do not know. But authors do not do thing on accident; it was no coincidence that the cat was there when Bigger shoved Mary into the furnace.

Question
When the cat hopped on Bigger's shoulder, did it really betray him? Will he try and rid the cat so he will not be found out?