Who had a reason to kill the victim? Does any particular person benefit - financially or romantically - from the victim's death?
Who had access to the murder weapon? Does any particular person have the unique knowledge, skill or physical ability necessary to use the murder weapon?
Who had a chance to kill the victim? Is any particular person unaccounted for (has no alibi) during the time the victim was killed?
Be sure to evaluate motive, means and opportunity for each suspect before filing for your arrest warrant: