If akazawa doesn't think it was writte nby the murdered policeman, why show the prosecutor the letter when she hasn't even taken on the case yet? Seems like he showed her the letter in order to shake her up and provoke her into telling someone else, to try and provoke her into action.
I hope this manga doesn't have too much girly shoujo shy romance between the heroine and the lawyer. I don't mind having romance , obviously there's going to be , but the author is dedicating way too many panels to the lawyer looking flustered while looking at the heroine. We get it. It's not appealling to keep hitting us over the head with it. And it isn't enjoy able romantic chemistry either. There are some stories with some couples that you can watch interact and fall in love and it's delightful to watch and other stories where couples fall in love and you think "bleh" because it's so saccharine and one-note.