did justine kill william

No, Justine was innocent of killing William.

Just in case you needed extra information, it was the creature that killed William.

"At this time a slight sleep relieved me from the pain of reflection, which was disturbed by the approach of a beautiful child, who came running into the recess I had chosen, with all the sportiveness of infancy. Suddenly, as I gazed on him, an idea seized me, that this little creature was unprejudiced, and had lived too short a time to have imbibed a horror of deformity. If, therefore, I could seize him, and educate him as my companion and friend, I should not be so desolate in this peopled earth.

"Urged by this impulse, I seized on the boy as he passed and drew him towards me. As soon as he beheld my form, he placed his hands before his eyes and uttered a shrill scream: I drew his hand forcibly from his face, and said, 'Child, what is the meaning of this? I do not intend to hurt you; listen to me.'

"He struggled violently. 'Let me go,' he cried; 'monster! ugly wretch! you wish to eat me, and tear me to pieces -- You are an ogre -- Let me go, or I will tell my papa.'

"'Boy, you will never see your father again; you must come with me.'

"'Hideous monster! let me go. My papa is a Syndic -- he is M. Frankenstein -- he will punish you. You dare not keep me.'

"'Frankenstein! you belong then to my enemy -- to him towards whom I have sworn eternal revenge; you shall be my first victim.'

"The child still struggled, and loaded me with epithets which carried despair to my heart; I grasped his throat to silence him, and in a moment he lay dead at my feet."