You can move to Connecticut or New York while on Medicaid but it will not be easy.
You will have to move to Connecticut or New York and then reapply for Medicaid.
Since each state evaluates its applicants independently from each other state, those who want to transfer their coverage must re-apply for Medicaid in the new state.
Further complicating matters is the fact that someone cannot be eligible for Medicaid in two states at the same time. Therefore, in order to apply for Medicaid in a new state, mom must first close out their Medicaid coverage with the old state.
Moreover, most states require you to move to the state and establish residency first and then apply for Medicaid.
While most states have unique requirements, normally their income and assets limits are very similar as are the level of care requirements.