Hmm. Okay lets see what the characters (not the audience) know.
Victim: Artist, lives a secluded life with only her dog, has a boyfriend no one knows about.
Killer: Boyfriend and unfaithful husband of another wife, killed his mistress in his own home.
What the police know:
Victim:
They know she was killed, they know she little social activity (seeing as how they did not know about her boyfriend), they know someone with glasses has been in her home, they know she did a portrait of someone with glasses and they know she placed a call within 10-block radius of the home of one of the members of the search party.
Killer:
They know he was one of the search part members, they suspect he planted her wallet when it was recovered, they know he wears glasses.
So since they cannot conclude that she made the call from the boyfriend's house there is no way to make that case in court. That is why it took the birth of a litter of Mutts to close the case, Grrl.