I was watching a movie last night on the Liftetime movie channel network, I have legal questions?

It was a movie based on a true story of this man who seems ok at first but ends up having quite the contrary. After marrying this girl, he ends up moving and ends up killing her, but when the daughter and sister of the victim starts to ask questions and does there own investigation because the police and FBI did nothing to help?? I want to know how is that because there is no body then there is no crime committed? I mean obviously if someone is disappeared do you just give up and don't look for them anymore? Then, another thing I want to know is why the police didn't search the guys house? Ok in the movie supposedly she left a note saying she was leaving, and when the guy admits he threw the note a way, why didn't the detective, go through the trash or ask if he put the trash out yet, or try to see where the note was, because there was no note. Ok then you have his family that obviously is hiding something and again the police and detective end up leaving and not getting anywhere? I just want to understand the judicial process in pointing someone to murder. If there is reasonable doubt that he did in fact have something to do with her disappearance then why not interrogate him. or try something besides the lie detector test which was pointed out in the movie as no admissible into court. Why is that? Thank you.