There are two types of dependents. Whether your child qualifies for either depends on some judgment calls on your part.
The first is a qualifying child. To be a qualifying child, the child needs to live with you more than half the year. If the child is expected to be living in another facility such as group home, permanently, the the child could not be your qualifying child dependent. If the group home residency is expected to be only temporary then yes, the child could be your dependent.
If not a qualifying child dependent, it's possible for him/her to be a qualifying relative dependent. The qualifying relative would not require the child to live with you. It would , however, require that you pay more then half the child's support for the year. If expenses for living at the group home are funded by a third part, such as Medicare or Medicaid, or other state program, it is very unlikely you could be providing more than 1/2 support for the year. If you pay the cost for the child to live at the group home, then yes, the child could be a qualifying relative dependent.
