The cops that arrested him said something like " He looks like that guy the New York Senator described. "
So Nathan called the cops to find his brother, which means he is not under arresst fir any crime, although lying in a pool of blood will raise questions.
I don't think you can find something sharp enough to cleave through a human skull without causing the victim to even flinch just lying around. I mean she didn't even show the slightest bit of impact motion, there was no transfer of kinetic energy.
I think her father really cares about her and does not want to see harm come to her. That is why he was willing to have Issac back on the H to paint the painting the may save her life.
.... and if he doesn't go back in time to save her, she dies, so he goes back in time to save her, so she lives, then he doesn't need to go back in time to save her, but becasue he doesn't she dies.......................... :p