Can the State Take Mom's House for Medicaid Reimbursement?

It depends on how your mother and sister owned the property. If they owned it as "tenants in common," then you must probate your mother's estate and her half of the property will be subject to claim by the state. If they owned it as joint tenants, the property will pass automatically to your sister free from claim by the state. Even in the first instance, if your sister has low income and lives in the house she may qualify for a waiver of the state's claim. These rules may be different in other states.