Some moments in the game hint that Bigby will later be accused by the real murderer and people will side with him according to choices we made.And there are a lot of these moments in episode 1:
-Whether or not you choose to be nice with Colin,Toad,Bufkin and even the woodsman.
-If you choose to reap off Grendel's arm,Woody tells you that you're a monster and the game says that he and Holly will remember that.
Maybe someone spies on Bigby in the beginning of the game when he talks to Faith on the street.He is seen giving her money (if you made that choice) and thus he looks like he is her last "client".Woody could testify that Bigby was the last person that saw Faith,thus making him the first suspect.
And later in the game Bigby is always investigating with Snow,it would be easy to accuse him since he is the last person that saw her.However he was in the bar at that moment so I don't know how the killer will manage to accuse him for that.It would also explain why there is a cop that appears to be spying on Bigby in the episode 3 image.What do you think ?