The Superior Court panel returned its decision Tuesday and will consider on Wednesday whether Gideon Omondi was insane at the time of the 2006 killing.
His defense attorney says Omondi was distraught about a custody fight and didn't know what he did was wrong.
He was also convicted Tuesday of trying to kill his son earlier by putting him in the trunk of his car and dousing it with gasoline.
Omondi pleaded not guilty by reason of insanity. If jurors find Omondi is insane, he will be sent to a state mental hospital. Otherwise he faces a minimum of 25 years to life in prison.