I enjoyed reading the opening chapters of your historical crime story. There is definitely an atmosphere of another era in an American town. The dialogue shows that well, I think. Also, the relationship between Gretchen and Eugene is disquieting enough that I'm desperate to find out more about their history.
As much as I found chapters 2 and 3 to flow well, the writing in chapter 1 sounded somehow less assured. In particular, the scene where Gretchen encounters the cop at her car. I wonder if tightening that scene might be all that's needed ?
I hope you won't think me presumptuous if I took the liberty of applying virtual scissors to that scene to illustrate what I'm trying to say by "tightening" it. Having the scene play out in less words, I guess I mean. Where I changed a sentence, I inked it in red. Only a suggestion, that goes without saying !