CMS regulations at 42 CFR 435.603(f)(2) provide that the parents would be included in the child's household in this situation. However, if the parents do not intend to continue to claim the child as a tax dependent for the following tax year, states may alternatively use the option provided at 435.603(h)(3) to consider the child's move to the live with another caretaker relative as a "reasonably predictable change in income" and apply the non-filer rules to the child at 435.603(f)(3). Under the non-filer rules, neither the parents nor the caretaker with whom the child is living would be included in the child's household for purposes of Medicaid and CHIP eligibility.
Note that to be claimed as a "qualifying child," children generally must live with their parents for at least half of the year (certain exceptions apply), but parents may also be able to continue to claim a child as a "qualifying relative." States are not expected to determine whether or not a parent is permitted to claim their child as a tax dependent or not, but states may wish to consult IRS Publication 501 to better understand the general requirements which must be met for a tax filer to claim another individual either as a "qualifying child" or "qualifying relative." IRS Publication 501 can be accessed at the following link: http://www.irs.gov/pub/irs-pdf/p501.pdf.
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