Should someone who suffers from a mental illness and has a criminal record be barred from having custody of children?

Should someone who suffers from a mental illness and has a criminal record be barred from having custody of children?

Five year old Phoebe Jonchuck was thrown to her death off a St. Petersburg Bridge by her own father, Jon Jonchuck.  Answer the following questions:  Was there a previous history with Jon Jonchuck by DCF?  Could this tragedy have been prevented?  Did Jonchucksuffer from a mental illness?  If so, what was the mental illness?  Did he receive treatment?  Is there any responsibility that the therapist has given the outcome of this case?  What type of treatment would have been effective if any with Jonchuck to have prevented this tragedy?   Did he have a criminal record?  Should someone who suffers from a mental illness and has a criminal record be barred from having custody of children?  What could have been done differently by DCF workers?  If you were asking questions of the DCF secretary Mike Carroll what would you want to know about his agencies response to this case?  Should he resign his post given the public outrage?  What measures could be taken to improve the operation of DCF in light of this tragedy?  The story can be found at the following link: http://www.nbcnews.com/news/crime-courts/john-jonchuck-accused-hurling-daughter-bridge-mentally-unfit-trial-n313461