Basically Alice is a little bitch and her sister Karen (played by a young Brook Shields) is a whiny spoiled brat who craves attention. Alice likes to fuck with her sister. For example, snatching her first communion veil and putting it on while her sister yelps. Who can blame her, being told her sister is the pretty one all the time. So when Karen is found dead and burning inside the organists bench all eyes turn toward Alice. Her parents insist she is innocent and an investigation ensues.
One final thought. A police detective makes an observation to his fellow officer that Alice is surely is a strange girl. I looked up the actress who played Alice and curiously enough her only other film cred is for Liquid Sky. So I concur that Alice truly is a strange girl.