Sarah's murder was premeditated. When Andrew broke up with her, she didn't know that his new love was in fact her sister Thelma. when questioned, Thelma was defensive when it came to Andrew and the break up. The threatening note was sent by Thelma, she was the only suspect that was left handed which explained the smudged writing. They both lured Sarah out. Armed with an axe from Andrews work, they waited until Sarah arrived at central park and hit her with it. Thelma had a key to Sarah's apartment and they moved her together.  Call it a crime of passion if you want, maybe they did do it for love. It's a lovely story... still murder.